To the bowl of a stand mixer with the dough hook attachment, add 3 cups flour, dry yeast, sugar, egg, and salt.
Heat milk until very warm (110°F to 120°F).
Add warm milk to the flour mixture. Knead for 2 minutes at medium speed, stopping to scrape the sides of the bowl as needed.
Add another ½ cup flour. Knead at medium speed for another 2 minutes.
Add remaining ½ cup flour. Knead. The dough should be very soft and pulling away from the sides of the bowl. (If the dough seems too wet you may need more flour. Add in ¼ cup increments until the dough has pulled away from the sides of the bowl while kneading.)
Cover with plastic wrap. Let rest for 30 minutes, or until doubled in size.
When ready, remove plastic wrap and punch down dough.
Spray a 9x13-inch baking dish with nonstick cooking spray.
Divide the dough into 16 equal-sized pieces and shape into balls. Place into the prepared baking dish. I was able to fit 12 rolls into the dish, leaving four left over. Place the extra rolls into a greased pie pan and bake as directed. (If you have a larger pan, you could bake all the rolls at once.)
Cover the rolls with plastic wrap. Let them rest for 30 minutes, or until doubled in size.
Preheat oven to 375°F.
Bake rolls for 16-17 minutes, or until golden brown.
Brush the warm rolls with melted butter. Sprinkle kosher salt on top if desired. Enjoy!