Whisk the yeast into the warm water in a small bowl and let it sit until bubbles start to appear.
In a separate bowl, whisk together the milk, melted butter, and sugar. Add the activated yeast mixture and whisk until everything is combined well.
Place the flour and salt in the bowl of your stand mixer fitted with the hook attachment. Add the milk mixture and knead on medium-low speed for 5-6 minutes.
Cover the bowl with a clean kitchen towel and let it stand at room temperature for about an hour, or until the dough has doubled in size.
Punch down the dough, divide it into 12 equal pieces, shape each piece into a ball, and place them in a greased 9x11 inch baking pan. Cover and let them rise again until puffed up, about 20-30 minutes.
Preheat your oven to 375°F (190°C). Beat the egg and use it to wash the tops of the rolls.
Bake for roughly 20 minutes or until they are golden brown.
Brush with additional melted butter right after they come out of the oven, if desired. Remove from the pan and serve warm.
Notes
Use warm water for activating yeast, and allow enough time for the dough to rise for optimal fluffiness.
Leftover rolls can be stored and reheated in the oven.