Heat some olive oil in a large skillet over medium-high heat.
Add the onions and cook for 5-6 minutes and season with salt.
In the bowl of a standing mixer, stir the yeast into the warm water ( about 120 degrees and let it sit for about 5-6 minutes.
Once the yeast is nice and foamy go ahead and beat in the hot milk, sugar, melted butter, salt, and egg.
Add the bread flour to the yeast mixture, and knead with the dough hook. Mix for 8-10 minutes until the dough is slightly tacky.
Add the granulated onion and 3/4s of the cooked onions.
Flour your work surface and knead the dough with your hands for a couple extra seconds
Place the dough in a greased bowl, cover and let it sit in a warm place for about an hour or until it doubles in size.
Place the risen dough on your floured work surface and divide the dough into 12 pieces.
Shape the dough pieces into dinner rolls by tucking the edges underneath.
Butter a 9 x 13 baking pan and place the balls of dough spaced a little apart. Cover and let it rise in a warm place for an additional 40 minutes or until doubled in size
Brush the risen balls of dough with the egg wash and top each roll with the remaining onions. Place in a preheated oven at 375 degrees F for 28 minutes or until fully cooked through.
Brush with melted butter and enjoy.