In bowl of stand mixer, combine warm water, 1/3 cup melted butter, yeast and sugar. Whisk together and let stand for 15 minutes until foamy.
Preheat oven to 300 degrees F. Once it hits temperature, turn oven off and crack the door.
Prepare baking sheet by greasing with butter or lining with silpat.
Add salt, egg, bread flour, and rosemary to mixer. Attach dough hook and stir on low speed until combined. Increase speed to medium and knead for 3 minutes. Dough will be very sticky.
Coat hands with additional flour and drop 12 balls of dough on baking sheet. They might be too sticky to form perfect balls - totally okay.
Place baking sheet in warm oven and allow bread to rise for 10 minutes.
Increase temperature to 400 degrees F. Bake rolls until golden brown, about 10 minutes.
Remove rolls from oven and spread tablespoon of butter on the tops of the rolls (it will melt as you rub it). Serve immediately or store in air tight container