Activate the yeast: In a large bowl, whisk warm milk, yeast, and 1 tablespoon of the sugar. Let sit 5–10 minutes until foamy.
Mix wet ingredients: Add remaining sugar, melted butter, egg, yolk, and vanilla.
Whisk smooth.
Add dry ingredients: In a separate bowl, combine 3 cups flour, salt, cinnamon, ginger, and nutmeg. Stir into the wet mixture along with the well-squeezed grated carrot.
Knead: Mix until a soft dough forms. Knead by hand on a lightly floured surface 6–8 minutes, adding up to 1/4 cup flour only if sticky.
The dough should be soft and slightly tacky, not wet.
First rise: Place in a greased bowl, cover, and let rise in a warm spot until doubled, about 60–90 minutes.
Prepare filling: Stir soft butter, brown sugar, cinnamon, ginger, and salt into a spreadable paste. Have nuts or raisins ready if using.
Shape: Punch down dough. Roll into a 12x16-inch rectangle.
Spread filling evenly, leaving a 1/2-inch border on one long side. Sprinkle nuts/raisins.
Roll and cut: Tightly roll from the opposite long side toward the clean border. Pinch seam to seal.
Cut into 12 even rolls using dental floss or a sharp knife.
Second rise: Arrange in a greased 9x13-inch pan. Cover and let rise until puffy, 30–45 minutes. Preheat oven to 350°F while they rise.
Bake: Bake 22–26 minutes until lightly golden and centers register about 190°F.
Don’t overbake—edges should be set, centers soft.
Make frosting: Beat cream cheese and butter until smooth. Mix in powdered sugar, vanilla, salt, and enough milk to reach a spreadable glaze.
Frost: Let rolls cool 10–15 minutes, then spread frosting over warm rolls so it melts into the swirls.