In a heatproof bowl, combine warm milk, water, melted butter, sugar, and salt. Stir well and let cool until the mixture is below 110°F (45°C).

Sprinkle the yeast over the warm liquid. Wait 5–10 minutes until foamy to ensure the yeast is active.

Gradually stir in 3 cups of flour. When the dough becomes too stiff to stir, turn it onto a lightly floured surface.

Knead the dough for 6–8 minutes, adding more flour as needed, until it’s smooth and elastic.

Place the kneaded dough in a greased bowl and cover with a damp towel. Let it rise in a warm spot for 45–60 minutes, until doubled in size.

Punch down the dough and divide it into 18 equal pieces. Shape each piece into a smooth ball and place on greased baking sheets.

Cover the shaped rolls and let them rise 30 minutes, until puffy and nearly doubled.

Preheat your oven to 375°F (190°C). Brush the tops of the rolls with the beaten egg for a golden finish.

Bake for 12–15 minutes, or until the rolls are golden brown. For extra indulgence, brush immediately with melted butter.