Heat milk to 115°F. Dissolve yeast and granulated sugar in warm milk. Allow to proof for 5-10 minutes. 

Add vanilla to melted butter. 

Meanwhile, in the bowl of a stand mixer, combine 4 cups flour, light brown sugar, salt, cinnamon and nutmeg. Prepare mixer with dough hook attachment. With mixer running on low, slowly add yeast mixture, followed by butter and vanilla. Add one egg at a time. Add finely shredded carrots. Increase speed, mixing until dough comes together. If dough is still sticky, add additional flour, one tablespoon at a time until dough comes together in a smooth ball. Transfer dough to a large greased bowl. Cover and allow to rise in a warm location for at least 60 minutes or until doubled in size. 

Lightly grease a 9x13-inch baking pan with baking spray. *See note. 

In a medium bowl, combine brown sugar and cinnamon. 

On a silicone counter mat, roll out dough to a 12-20-inch rectangle. Brush entire surface with melted buter. Sprinkle well with brown sugar and cinnamon mixture. Starting at one of the short ends, begin rolling the dough into a log. Pinch to seal ends. Using a sharp knife, carefully slice dough log into desired number of rolls. **See note. Space evenly in prepared pan. Cover loosely and allow to rise in a warm location for an additional 60 minutes. 

Preheat oven to 350°F. 

Bake for 30-40 minutes or until internal temperature reaches at least 200°F. Allow rolls to cool for 20-30 minutes before adding icing. 

To create icing, in a large bowl or stand mixer, beat together cream cheese and butter until light and fluffy. Mix in vanilla and powdered sugar. Add in milk, one tablespoon at a time, until desired consistency is reached. Pour or spread glaze over rolls.