Carrot halwa is a kind of "carrot pudding" made in India. It has the bright orange color and slight crunch, sometimes, of fresh carrots, but cooked with milk and lots and lots of sugar. It's unusual, and delicious. Here's one more recipe that includes beetroot. Another take on this theme are these Carrot Cups, individual kosher puddings.
This Chantenay Carrot Soup only needs about six ingredients. For other simple side dishes, try Carrots with Garlic and Yogurt, Braised Carrots with Thyme, or Cooked Carrot Salad with Pine Nuts and Golden Raisins, from one of Lidia Bastianich's cookbooks.
For a vegetarian main course, try this Soba Noodle Salad with Carrot and Zucchini; for the meat-eaters, this Spinach and Carrot Stuffed Flank Steak looks hearty and filling.
Happy beta carotene!