In the bowl of a stand mixer, add the yeast, warm milk, melted butter and sugar and stir together. Let it sit for 5 minutes until it is foamy.
Add the egg, rosemary, and salt and mix to combine everything.
Slowly add the flour, 1 cup at a time until the a soft dough forms. If the dough is too sticky, add a little more flour.
Using the dough hook attachment, knead the dough on the stand mixer for 5 minutes until it is soft and elastic.
Transfer the dough to a lightly floured surface and form it into a large ball. Divide the dough into 12 portions and roll out each portion into a ball.
Preheat oven to 425F.
Lightly grease a skillet or baking pan and arrange the balls of dough in it. [The dinner rolls will expand while they bake so allow for some room in between the balls of dough.]
Cover the dinner rolls with a clean kitchen towel and let them rise for 10 minutes.
Melt 2 tablespoons of butter and stir in the remaining rosemary. Lightly brush the dinner rolls and then place them in the oven to bake for 18-20 minutes or until they are golden brown.
Once out of the oven, brush the dinner rolls with the remaining melted butter.