In a mixing bowl, combine the warm milk and sugar. Sprinkle the yeast over the top and let it sit for about 5-10 minutes until foamy.
Add the melted butter and egg to the yeast mixture and stir until combined.
Gradually add the flour, one cup at a time, along with the salt. Mix until a dough forms.
Knead the dough on a floured surface for about 5-7 minutes until it becomes smooth and elastic.
Place the dough in a greased bowl and cover it with a kitchen towel or plastic wrap. Let it rise in a warm place for about 1 hour, or until doubled in size.
Once risen, punch down the dough and divide it into 12 equal pieces. Roll each piece into a ball.
Place the dough balls onto a lined or greased baking sheet, spacing them about 2 inches apart.
Cover the rolls with a towel and let them rise again for 30 minutes, or until puffy.
Preheat the oven to 375°F (190°C).
Bake the rolls for 15-20 minutes, or until they are golden brown on top.
If desired, brush the hot rolls with melted butter right after taking them out of the oven.
Serve warm and enjoy your delicious homemade dinner rolls!