To the bowl of a stand mixer with the dough hook attachment, add 3 cups of flour, yeast, sugar, rosemary, and salt. Mix to combine.
Add warm milk and egg to the flour mixture. Knead for 2 minutes at medium speed.
Add another ½ cup flour. Knead at medium speed for another 2 minutes.
Add remaining ½ cup flour. Knead until the dough is pulling away from the sides of the bowl. If the dough seems too wet, add more flour in ¼ cup increments until the dough has pulled away from the sides of the bowl while kneading. If the dough is too dry, add more water in ¼ cup increments.
Place dough in a greased bowl. Cover and let rise for 45 minutes, or until doubled in size.
When ready, punch down the dough.
Spray a 9×13-inch baking dish with nonstick cooking spray.
Divide the dough into 12 equal-sized pieces and shape into balls. Place into the prepared baking dish.
Cover the rolls and let them rise for 30 minutes, or until doubled in size.
Preheat oven to 375°F.
Bake the rolls for 18-22 minutes, or until golden brown.