In a small bowl, combine the warm milk and 1 tablespoon of sugar. Sprinkle the yeast over the mixture and let it sit for about 5-10 minutes until it becomes frothy.
Mix the Dough:
In a large mixing bowl or the bowl of a stand mixer fitted with a dough hook, combine 3 cups of flour, remaining sugar, and salt.
Add the frothy yeast mixture, melted butter, and egg to the dry ingredients. Mix until a rough dough forms.
Kneading:
If using a stand mixer, knead the dough on a medium-low speed for about 5-7 minutes. If kneading by hand, transfer the dough to a floured surface and knead for 8-10 minutes until smooth and elastic.
Gradually add the remaining 1 cup of flour as needed, but the dough should remain slightly sticky.
First Rise:
Place the dough in a greased bowl, turning once to coat the dough with oil. Cover the bowl with a clean kitchen towel or plastic wrap.
Allow the dough to rise in a warm, draft-free place for about 1 to 1 1/2 hours, or until it doubles in size.
Shaping the Rolls:
Once the dough has risen, gently punch it down to release the air. Turn it out onto a lightly floured surface.
Divide the dough into 12 equal portions and shape each portion into a smooth ball.
Place the shaped rolls in a greased 9×13-inch baking pan or on a parchment-lined baking sheet, leaving a little space between each roll.
Second Rise:
Cover the rolls loosely with a clean kitchen towel and let them rise for an additional 30-45 minutes, until they are puffy and nearly doubled in size.