In a large mixing bowl, add warm water, yeast, sugar and olive oil.
Stir together and set aside about 5 minutes or until yeast starts to bubble.
Mix in egg and stir in 1 cup of flour.
Add salt and an additional 2 cups of flour, Parmesan cheese and rosemary, stirring until well combined.
Add flour 1/2 cup at a time until dough pulls away from sides of bowl.
Pour onto a well floured surface.
Knead for 5 minutes, adding flour about 1/4 to 1/2 cup at a time as needed.
Dough should be flexible but not sticky.
Shape into rolls and place in a well-greased baking pan. I used 2 small pans.
Cover with a flour sack towel and allow to rise for about 30 minutes to an hour.
Preheat oven to 400 degrees F.
Bake rolls for 12-15 minutes or until golden brown.
While rolls are baking, add butter and minced garlic clove to a small saucepan.
Cook over low heat for 5-7 minutes.
Remove from heat and set aside.
When you remove rolls from oven, immediately brush them with garlic butter and devour!