Cut the onion into fine dice, and set aside. Melt the butter in a frying pan, add the onion, and sauté over medium-low heat for 15 to 20 minutes, or until the onion is light brown. Stir in the sugar, and sauté an additional 5 minutes. Let cool to room tem
In a mixing bowl, dissolve the yeast in the warm water. Add the milk, egg, butter, sugar, salt and flour. Stir to combine, then knead the dough till it's smooth and elastic, 5 to 10 minutes. Place the dough in a lightly greased bowl, turning to coat all s
Punch the dough down, and knead in the sautéed onions. This is easily done with a mixer (or in a bread machine), but it's also a fairly simple matter to do it with your hands.
Shape the dough into a ball, and let it rest for 10 minutes. Roll or pat it out into a 3/4-inch thick circle.
Using a regular-sized tuna can (or other can or cutter about 3 1/2 inches across), cut the dough into nine rounds. Transfer the rounds to a baking sheet, leaving about a 1-inch clearance between them. Brush the rounds with the glaze, which you've made by
Bake the rolls in a preheated 350°F oven for 20 minutes, or until they're golden brown. Remove from the oven, and cool on a wire rack.