1. Combine warm milk (110°F), sugar, and yeast in a small bowl. Stir gently and let sit for 5 to 10 minutes until foamy.

2. Whisk together flour, salt, cinnamon, and nutmeg in a large bowl. Add melted butter, egg, and activated yeast mixture. Stir until a shaggy dough forms, then knead by hand for 8 to 10 minutes or use a stand mixer with dough hook for 5 to 7 minutes until smooth and elastic.

3. Place dough in a greased bowl, cover with a clean towel, and let rise in a warm spot for 1 to 1.5 hours until doubled in size.

4. While dough rises, mix grated carrots, brown sugar, softened butter, cinnamon, nutmeg, and nuts if using in a bowl. Set aside.

5. Punch down risen dough gently and roll out on a floured surface into a 12×16-inch rectangle about 1/4-inch thick. Spread carrot filling evenly over dough, leaving a 1/2-inch border on one long edge.

6. Starting from the long edge opposite the border, roll dough tightly into a log. Pinch the seam to seal. Using a sharp knife or dental floss, slice into 12 equal rolls.

7. Arrange rolls in a greased 9×13-inch baking dish, cover loosely, and let rise for 30 to 45 minutes until puffy.

8. Preheat oven to 350°F. Bake rolls for 25 to 30 minutes until golden brown and cooked through.

9. While rolls bake, beat cream cheese and butter until smooth. Gradually add powdered sugar, vanilla, and enough milk to reach spreading consistency. Spread icing generously over warm rolls right out of the oven.