Activate Yeast: Combine the warm water, 1 teaspoon of sugar (from the 2 tbsp), and the yeast in a small bowl. Let it sit for 5–10 minutes until foamy.
Mix Dough: In a mixing bowl, combine flour, remaining sugar, and salt. Add the yeast mixture, warm milk, melted butter, and egg. Mix until the dough comes together.
Knead Dough: Knead the dough on a lightly floured surface for 8–10 minutes, or use a stand mixer for 5–6 minutes, until smooth and elastic.
First Rise: Place the dough in a lightly greased bowl, cover, and let it rise in a warm place for 1–1 ½ hours, or until doubled in size.
Shape Rolls: Punch down the dough and divide it into 9 equal pieces. Shape each piece into a ball and place them evenly in a greased 8x8-inch pan.
Second Rise: Cover and let the rolls rise again for 30–40 minutes, until puffy.
Bake: Preheat your oven to 375°F (190°C). Bake for 15–18 minutes, or until golden brown.
Brush with Butter: Brush the tops with melted butter while warm for extra softness and shine.