2 tablespoons active dry yeast
1/2 cup plus 1 tablespoon sugar, divided
1/2 cup warm water, 105°F to 115°F
1 cup whole milk
1 cup (2 sticks) unsalted butter, divided
2 large eggs, room temperature and lightly beaten
2 teaspoons fine sea salt
5 cups all-purpose flour, plus more if needed
24 smoked cocktail sausages
Additional flour, for rolling
Sprinkle yeast and 1 tablespoon sugar over the warm water and let sit until foamy, about 10 minutes.
Meanwhile, heat the milk and 1/2 cup (1 stick) butter in a small saucepan over medium-low until butter is just melted. Remove from heat and stir in the remaining 1/2 cup sugar until dissolved.
Combine the milk mixture, yeast mixture, eggs, and salt in a large mixing bowl. Stir in 4 cups of flour and mix well. Add the remaining flour 1/2 cup at a time, until a ball of dough forms — the dough should be smooth and fairly sticky, but not tacky; if it seems to wet, add another 1/2 cup of flour.
Transfer the ball to a large greased mixing bowl. Cover with plastic wrap or a damp tea towel and set it in a warm, draft free place. Let the dough rise until doubled in size, about 1 1/2 hours.
Preheat oven to 350°F. Place cocktail sausages on a baking sheet and cook for 20 minutes. Remove from the oven and allow to cool. Thoroughly blot with a paper towel to remove any excess grease.
Meanwhile, grease two 9-inch cake pans or disposable aluminum rounds. Turn out the dough onto a lightly floured surface. Sprinkle a little bit of flour on top of the dough and roll to 1/2-inch thickness. Using a floured biscuit cutter, cut dough into 2-inch rounds.
Gently press each round into an oval shape, place 1 cocktail sausage in the center, and fold the dough around to form a half moon. Gently press the very center front to seal shut. Set aside and continue with remaining rounds.
Melt the remaining 1/2 cup (1 stick) butter. Using a silicone pastry brush, lightly coat each roll with butter. Starting on the outside and working your way in, place the rolls, seam side out, into the greased pans (about 12 rolls per pan, see above image). Cover the pans with plastic wrap or a damp tea towel and a let rise in a warm, dry place until doubled in size, 30 minutes to 1 hour.
Preheat oven to 375°F. Bake the rolls, uncovered until just barely golden, 15 to 20 minutes. Remove rolls from the oven and brush with any remaining melted butter. Serve hot.
To make rolls the night before: Arrange rolls in pans and allow to rise as directed. Refrigerate, covered, up to 24 hours. Let stand at room temperature for 30 minutes to an hour while oven is preheating. Bake and serve as directed.
To make rolls and freeze: Arrange rolls in pans and allow to rise as directed. Tightly wrap each pan in a layer of plastic wrap followed by a layer of aluminum foil. Rolls can be frozen for up to one month. To cook, remove from freezer and let stand at room temperature for 2 to 2 1/2 hours. Bake and serve as directed.