In the bowl of a stand mixer fitted with the dough hook, whisk the warm milk, yeast and 1 tablespoon of sugar. Allow the mixture to sit for about 5 minutes. The mixture should foam if the yeast is alive.
Add the remaining sugar, the egg, butter, salt, and 1 cup flour. Beat on low speed for about 30 seconds, scraping down the sides of the bowl with a spatula. Add another cup of flour and beat on medium speed for a couple of minutes. Add the rest of the flour and beat on medium speed until the dough comes together and pulls away from the sides of the bowl.
Keep the dough in the mixer and beat for an additional 2 minutes or knead by hand on a lightly floured surface for 2 minutes.
Transfer the dough to a lightly greased bowl with oil or nonstick spray. Turn the dough to coat all sides with the oil. Cover the bowl with a clean kitchen towel or with plastic wrap. Allow the dough to rise at room temperature for 1 1/2 to 2 hours or until double in size.
Grease a 9 × 13-inch baking pan. You can also bake the rolls on a baking sheet lined with parchment paper or in a cast iron skillet.
Remove the towel or plastic wrap and deflate the dough by punching it down lightly. Divide the dough into 14-16 equal pieces. Shape each piece into a smooth ball and place each one in the prepared baking pan.
Cover the shaped rolls with a clean kitchen towel or plastic wrap. Allow them to rise for about 45 minutes to 1 hour at room temperature.
Meanwhile, adjust the oven rack to a lower position and preheat the oven to 350 degrees Fahrenheit.
Bake for 20-25 minutes or until golden brown on top, rotating the pan halfway through. If you notice the tops browning too quickly, loosely tent the pan with aluminum foil.
Remove from the oven, brush with butter and allow rolls to cool for a few minutes before serving.
Cover leftover rolls tightly and store at room temperature for 2-3 days or in the refrigerator for up to 1 week.