Activate yeast: In a small bowl, combine warm water, yeast, and 1 teaspoon sugar. Let it sit for 5–10 minutes until foamy.
Warm the milk: In a saucepan, heat milk until warm (not hot). Stir in softened butter and sugar until melted. Allow to cool slightly.
Mix wet ingredients: In a large mixing bowl, whisk together the milk mixture, egg, and salt. Add the yeast mixture and stir to combine.
Add flour gradually: Mix in 3 cups of flour, one cup at a time, stirring until the dough begins to form. Continue adding flour until soft and slightly sticky.
Knead the dough: Transfer the dough to a floured surface and knead for 5–6 minutes until smooth and elastic.
First rise: Place dough in a greased bowl, cover with a clean towel, and let rise in a warm place for about 1 hour or until doubled in size.
Shape rolls: Punch down the dough and roll it out to ½-inch thickness. Cut into squares or rounds using a sharp knife or biscuit cutter.
Second rise: Arrange rolls on a parchment-lined baking sheet, cover, and let rise again for 30 minutes.
Bake: Preheat oven to 350°F (175°C). Bake rolls for 12–15 minutes or until golden brown.
Butter finish: Brush freshly baked rolls with melted butter while still warm.