Make a big batch of beef piroshkis and freeze them? That still would only use up a pound or two. Honestly I think I'd see if friends or neighbors wanted to buy or trade for some of it!

Make a couple lasagnas to freeze!

It should keep for some time...you do have a deep freeze, right?

PIzza, shepherd's pie, stuffed peppers...

#1. You need to assess how much ground beef you would use over the next year. Keep that to use. Hopefully, you have a big enough freezer to keep it in!
#2. Give the rest to friends or family or even better to your local food bank or homeless shelter. My husband and I feed our local homeless camp community once a month with dinner (about 25-30 members). They love any meal with beef! They are hard working, sober and democratic....and very grateful for the home cooked meals.
Good luck!

Donate to a soup kitchen for a tax write off?

Ravioli, empanadas, stuffed peppers, meat sauce, nachos, pasties, enchiladas, italian wedding soup.

When we're talking THAT much excess food I would honostly donate alot of it. There are plenty of orginizations that could really use it!

If you're buying shares of beef, you must have the freezer space to store it, right? 50 pounds of hamburger = 1 meal a week for not quite a year. Unless you're only making 2 different things (which you said you're not) then spacing hamburger-based meals out, instead of having it every night, should by itself cut the monotony.
Taco meat can be tacos, or it can go on a salad, or just in a bowl with beans and salsa.
Sloppy joes?
There are a million different varieties of meatloaf, try some different ones out, or make stuffed peppers.
Do a Google search for "meatza."
My dad did Atkins when I was in high school, so we had a LOT of dinners that were just hamburger patty + side dish. It's perfectly do-able if you get creative with the side dishes.
Most Asian-style dumpling recipes call for ground pork, but I bet beef would work, it'd just be a bit stronger-flavored. "Feast of Fiction" on You-Tube has an episode with a pretty tasty dumpling recipe that I've used more than once.
Actually, a lot of Asian recipes also call for ground pork in a sauce, and I bet it would work there, too, if it's a fine enough grind. Think green beans with pork (beef) sauce, or Chinese 5 spice hamburger and rice.
And there's always pizza topping, spaghetti sauce, lasagna, any of a gazillion different casseroles....

lettuce wraps, meatloaf stuffed with chive & onion cream cheese, different kinds of meatballs (greek w/ yogurt sauce)

If you are tired of it, and want to get rid of part of it, decide how much to sell, determine a fair price and post to social media. I bought a lamb a couple years ago, and sold chops, etc. to friends.

If you have the freezer space, properly packed that ground beef should be good for one year. And as another poster stated, that's only one meal per week.

Here's a recipe using ground beef that's a little different:

LAHMAGINE (SMALL MEAT PIZZA)

Dough

1 pkg. (2 ½ tsp. active dry yeast)
½ tsp. sugar
1 c. warm water
3 ½ -4 c. all-purpose flour
2 tsp. salt
¼ c. vegetable oil

Topping
3 tbsp. olive oil
1 lb. ground beef or lamb
3 onions, finely chopped
1 red pepper, chopped
½ tsp. ground cumin
½ ground allspice
¼ tsp. ground cinnamon
1 tbsp. tomato paste
Salt
Freshly ground black pepper
Cornmeal for sprinkling

In a small bowl, dissolve the yeast and sugar in the warm water and let stand until the mixture begins to bubble, about 5 minutes. In the bowl of a stand-mixer, combine 2 cups of the flour with salt, oil, and yeast mixture and beat at low speed to combine. Gradually add the rest of the flour until the dough is firm, holds together well and cleans the sides of the bowl. Turn the dough out onto a lightly floured board and knead until it is smooth and elastic, about 10 minutes, adding flour as necessary to keep the dough from sticking. Place the dough in a large, lightly oiled bowl and turn once to coat. Cover with a towel and let rise until doubled in size, about 2 hours.
Heat the oil in a large skillet over medium heat. Add the meat and onions and cook, stirring often and breaking the meat up with a wooden spoon, until the onions are soft and translucent and the meat is browned. Add the red pepper and cook, stirring often, for 5 minutes. Add the spices and the tomato paste, stir to combine and cook for 2 minutes. Remove from heat and let cool.
Preheat oven to 475F. Sprinkle several baking sheets with cornmeal. Punch down the dough and cut into 8 equal pieces. Roll each piece into a round about 1/8th of an inch thick and about 5 inches in diameter. Place the rounds on the prepared baking sheets. Spread 2 ½ tbsp. of the topping over each round, leaving ½ inch edge. Bake until the bottoms of the rounds are crisp and the edges are golden brown, about 12 minutes. Serve hot.

This is a great soup recipe that calls for ground beef, I make it a lot, kids love it.
1 pound ground beef
1 cup chopped onion
64oz V8
2 10.5 ounce cans condensed cream of celery soup
1 tsp sugar (to taste)
3 cups shredded carrots (the bagged matchstick carrots give a heartier texture but cost more)
Brown meat & onion, add everything except the cream o soups, simmer on low for an hour. Add creamed soup and stir/simmer until welll combined. Freezes beautifully and reheats easily.

Just out of curiosity I went to a popular recipe site, & searched 'ground beef'. 2917 entries popped up. Even accounting for all of the multiples, that should keep you busy for a while. :)

there are a lot of Indian and Pakistani dishes that use ground beef like sheekh kabab and chapli kabab etc

Sloppy joes freeze amazingly well. Also, chimichangas-bake a bunch then you can freeze them and microwave easily. Meat sauce is also yummy--and you can't make a little.

You can also make and freeze meals for people for holiday gifts. Say, a busy sibling or parent who likes something easy to heat up?

I would share it with others, otherwise, if you over do it, you might get sick of beef for a long while.

How about mapo tofu?

Larb! Most thai places make a ground meat salad which is usually chicken or pork, but I bet beef would be delicious, too =)

http://www.foodinaminute.co.nz/Recipes/Thai-Larb

I add green onions and fresh cilantro to mine and serve it with a cucumber / cashew salad.

I would trade with a local food producer for something you'll use more often... Perhaps a discount on next year's CSA, or a fresh loaf of bread a week. I'm a piano teacher, and I would accept beef (or venison!) instead of pay for a lesson or two! :)

As a hobby farmer, I raise a lot of our own food. Depending on how old your meat is, I would sit on it. You will be surprised with how fast you go through it. If its getting up there in age, you can always give it away to your local shelter or church or you can trade it for work/services. People are always grateful for free organic meat. If you are looking for something interesting to cook, try Russian food. There are a lot of interesting things that you can do with it if you go the Russian way. Also, if you season it correctly, you can substitute ground sausage with your organic ground beef. That in turn will open up a ton of possibilities....which then leads back to my first statement....you will be surprised with how fast you go through it.