Stir yeast, 1/2 teaspoon sugar, and water into a mixing bowl. Let sit for ten minutes until it’s foamy and all the yeast is dissolved.
In the mixing bowl, stir in milk, brown sugar, sugar, eggs, vanilla, and salt. In a smaller separate bowl, stir together flour, cinnamon, nutmeg, and ginger. Add flour to the mixing bowl slowly and mix with dough hook for 4-5 minutes until dough is soft and well-combined.
Add softened butter and let the dough hook beat it into the dough. If they dough is very sticky, add another 1/4-1/2 cup flour. It’s okay if the dough is a bit sticky though. Beat with dough hook for another 4-5 minutes. Finally mix in grated carrots right at the end.You can make this dough without a stand mixer. Just combine the dough ingredients in the same order as above in a large mixing bowl and mix the dough vigorously with a wooden spoon. Then switch to your hands. If your hand is slightly wet it won't stick to the dough.
4) When dough is soft (it is okay if it's a bit sticky) Add dough to a clean metal bowl and dust with flour. Cover and let rise for two hours until it doubles in size.
Filling and shaping Cinnamon Rolls:
Mix filling ingredients in a small bowl and set aside.
Turn dough out onto a floured surface. Roll into a large rectangle. It should be about twice as long as it is wide so 12×24 is a good goal. Sprinkle filling over the surface of the dough. Spread the paste around until it is evenly distributed.
Roll dough starting from the short end so you are creating as many layers as possible. Roll tightly and once rolled, try to even out the roll so each part is the same thickness.
Cut rolls into 8 even pieces and add to a large, lightly buttered baking dish.Cover and let rise for an hour.
Baking and Icing Rolls
Bake rolls in a preheated 375-degree oven for 35-40 minutes until they are nicely browned around the edges and the center roll is cooked through. You can test this with a toothpick or tester.
Let rolls cool for about 30 minutes and then drizzle with icing.These are best served warm. If you are serving them the next day, it’s not a bad idea to microwave them for 10-15 seconds just to warm them up.