Warm the milk until it is about 110°F. Mix in the yeast, sugar, and one cup of the flour. Cover the bowl with a clean kitchen towel and set it aside in a warm place for about 30 minutes.
Add the eggs, melted butter, and salt to the dough mixture. Mix in the remaining 2 cups of flour in small portions. (Depending on the brand of flour, you may need up to one extra cup here).
Knead the dough in a stand mixer for about 10-15 minutes, or until it becomes elastic. The dough will be soft and slightly sticky. Cover the dough and let it rise for about an hour.
Punch down the risen dough and divide it into 12 equal portions(about 80 grams each). Shape each portion into a tight, round ball.
Arrange the rolls seam side-down in a parchment lined 9x13 inch baking pan. Cover the rolls with greased plastic wrap and let them rise for another hour.
Preheat the oven to 350°F. Make the egg wash by whisking the egg and one teaspoon of water together in a small bowl. Brush the rolls with the egg wash using a pastry brush.
Bake the rolls for 25-30 minutes, or until they are golden brown. Allow them to cool slightly, then dig in and enjoy!
Video
Notes
Note: You have the option of making 12 or 16 rolls! In order to get equally sized rolls, I use a scale to weigh out each ball of dough. For 12 dinner rolls, each dough ball should weigh about 80 grams. For 16 rolls, ~60 grams. You'll need an additional baking sheet or pan if you make more than 12 rolls. I used individual ramekins for the extra rolls, but use whatever baking dish you have on hand.