Activate yeast and combine liquid ingredients:Whisk the yeast into the warm water in a small bowl and set aside until bubbles start to appear on the surface. In the meantime, whisk together the milk, melted butter and sugar. Add the activated yeast mixture and whisk until combined.
Make dough:Add the flour and salt to the bowl of your stand mixer fitted with the hook attachment. Add the milk mixture, then knead on medium-low speed for 5-6 minutes, or until you have a smooth ball of dough. Add an extra tablespoon of flour if your dough feels too sticky!
Rise:Cover the bowl with a clean kitchen towel and let stand at room temperature for 1 hour, or until doubled in size. Punch down, then divide dough into 12 equal pieces; shape into balls. Place in greased 9x11 inch baking pan. Cover and let rise at room temperature until big and puffed up, about 20-30 minutes.
Bake:Heat the oven to 375°F. Beat the egg and egg wash the top of the rolls (you will most likely not use the entire egg; don't add too much or you'll have scrambled eggs on top of your rolls). Bake for around 20 minutes or until done. Brush with additional melted butter right as they come out of the oven, if you like. Remove from the pan and serve warm.