Dough: In a large mixing bowl, combine flour, cinnamon, ginger, nutmeg, and salt. Stir until well mixed, then set aside while you prepare the yeast mixture.
Proof the Yeast: Warm the whole milk according to the packet instructions—this should be around 110°F. It should feel warm to the touch, but not hot. Add the active dry yeast and 2 tablespoons of sugar to the milk and stir. Let it sit for about 5 minutes until it becomes frothy. This indicates that your yeast is active.
Mix the Dough: In the bowl of a stand mixer fitted with a paddle attachment, combine the yeast mixture with the remaining granulated sugar, egg and yolk, and butter. Beat on medium to medium-high speed for about 90 seconds until well combined. It’s normal for the mixture to look a bit lumpy.
Add Dry Ingredients: Turn the mixer to low and gradually add the dry ingredient mixture, one cup at a time. After all the flour is incorporated, scrape down the sides of the bowl and mix further.
Add Carrots: Mix in the grated carrots at the lowest speed for about 2 minutes. The dough will begin to pull away from the bowl and form a ball, indicating it’s ready for kneading.
Knead the Dough: Replace the paddle attachment with the dough hook, and knead on the lowest speed for about 8 minutes. If kneading by hand, transfer the dough to a lightly floured surface and knead for 10 to 15 minutes.
Check the Dough: After kneading, check the dough by gently pressing it with a clean finger. It should spring back slowly and feel tacky but not sticky. If it's too sticky, add a little more flour, one tablespoon at a time.
First Rise: Spray a large bowl with cooking spray or grease it with a bit of oil. Place the dough ball inside, cover with plastic wrap, and let it rise in a warm place for 1.5 to 2 hours, or until it’s doubled in size. If your kitchen is cool, consider placing it in a sunny spot.
Prepare the Filling: In a small bowl, combine brown sugar, cinnamon, ginger, and nutmeg. Mix well with a fork. Make sure your butter is very soft for easy spreading.
Punch Down and Roll Out: Once the dough has risen, punch the air out and transfer it to a floured surface. Roll it out into a rectangle, approximately 12 inches by 18 inches. Spread the soft butter over the dough, then evenly sprinkle the spiced sugar mixture on top. Scatter the grated carrots on top and gently press them down.
Roll Up: Starting from the longer side, roll the dough into a log shape and pinch the seam to seal it.
Slicing: Cut the log in half, then slice each half into 6 equal pieces. A sharp serrated knife or unflavored dental floss works wonders for clean cuts.
Second Rise: Grease a 9×13-inch baking dish and place the rolls inside. Cover them and let them rise in a warm spot for about 30 minutes, until they puff up noticeably. You can preheat the oven to 350°F at this point if you're ready to bake.
Baking: Bake the rolls for 30 to 35 minutes or until golden brown. A toothpick inserted in the center should come out clean. If you have a digital thermometer, check that the internal temperature is between 190°F and 200°F.
Frosting: While the rolls are baking, make your frosting by beating together cream cheese, confectioners' sugar, butter, vanilla, and an optional pinch of salt until creamy and fluffy. Adjust the thickness with more sugar if desired.
Serve: Frost the warm rolls directly from the oven for a melty effect or wait a few minutes for a thicker glaze. Optionally, top with chopped nuts for added texture and flavor.
