In a small bowl, combine the yeast and the sugar. Add warm milk and stir until dissolved. Let the yeast mixture sit for about 10 few minutes until frothy.
Add half of the flour and the salt to a mixer and add the yeast mixture. Turn the mixer on low and mix until the flour is combined. Keep on mixing while adding the remaining flour in, a 1/4 cup at a time until the dough pulls away from the sides of the mixer. This is when you know you have added enough flour—it's okay if you have flour remaining.
Turn the mixer off, cover the bowl with a kitchen towel, and let the dough rise until doubled in size.
Once your dough has doubled again, sprinkle flour on your counter and hand knead the dough. Using a knife or a pizza cutter, divide dough into 15 pieces of dough, then use your hands to shape dough into evenly shaped balls and place in a lightly greased 9" x 13" baking dish. Cover the rolls gently with a kitchen towel and let rise again in a warm place until doubled.
While the rolls rise, preheat your oven to 350 degrees F.
Once the rolls have doubled in size, whisk together the egg and water and brush over the dough balls using a pastry brush.
Bake in your preheated oven for 12-15 minutes, or until lightly golden brown.
Remove from the oven and brush with melted butter before serving warm. Enjoy!