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Activate the yeast: In a large bowl, combine the warm milk, sugar, and yeast. Let stand for 5-10 minutes until foamy.
Combine dry ingredients: In a separate bowl, whisk together the flour and salt.
Combine wet and dry ingredients: Add the flour mixture to the yeast mixture, along with the softened butter and beaten egg. Mix until a shaggy dough forms.
Knead the dough: Turn the dough out onto a lightly floured surface and knead for 5-7 minutes, or until smooth and elastic. You can also use a stand mixer with a dough hook for this step.
First rise: Place the dough in a lightly oiled bowl, turning to coat. Cover with plastic wrap or a clean kitchen towel and let rise in a warm place for 1-1.5 hours, or until doubled in size.
Shape the rolls: Punch down the dough and turn it out onto a lightly floured surface. Divide the dough into 12-15 equal pieces. Shape each piece into a smooth ball.
Second rise: Place the rolls in a greased 9×13 inch baking dish. Cover and let rise for 30-45 minutes, or until nearly doubled in size.
Bake: Preheat oven to 375°F (190°C). Brush the rolls with the melted butter. Bake for 15-20 minutes, or until golden brown.
Cool and serve: Let the rolls cool slightly in the pan before serving.

For extra buttery rolls: You can brush the rolls with melted butter again after they come out of the oven.
For sweeter rolls: Add an extra tablespoon or two of sugar to the dough.
For a richer flavor: Use whole milk instead of regular milk.
For garlic rolls: Mix minced garlic into the melted butter used for brushing.
Herb Rolls: Add dried herbs like rosemary or thyme to the dough or sprinkle on top before baking.