Sauté the diced onions with butter (or duck fat).
Mix and knead all of the dough ingredients—by mixer or bread machine—to make a soft, smooth dough.
Cover the dough and let it rise for 1 to 2 hours or until it's nearly doubled in bulk.
Gently deflate the dough and divide it into 30 pieces. (Each piece will weigh about 4 1/2 ounces on a kitchen scale.) Shape each piece into a round ball. Flatten the balls to about 3" across. Place the buns on a lightly greased or parchment-lined baking sheet, cover, and let rise for about an hour, until noticeably puffy.
Brush the buns with the egg wash.
Bake the buns in a preheated 375°F oven for 15 to 18 minutes, until golden. Remove them from the oven.
Cool the buns on a rack.