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Step 1
Place warm water (about 100-110°F) into the bowl of a stand mixer fitted with the dough hook. (The easiest way to test the water is using an instant read thermometer, but if you don’t have one, think hot bathwater.) Sprinkle the yeast into the water, then add the salt and sugar. Stir with a wooden spoon. Let rest until it bubbles, about 5 minutes.
Step 3
In another bowl or large measuring cup, whisk eggs and oil together. Add the egg mixture to the yeast mixture along with 1 cup of the flour. Start the mixer and then slowly add rest of flour, stirring in gradually. Run the mixture for about 5-10 minutes or until the dough is elastic. The dough will be slightly sticky and very soft. Turn it out onto a floured board and knead it a few times until it is no longer sticky.
Step 5
Place the dough into a bowl that’s been sprayed with nonstick cooking spray. Let rest until doubled.
Step 7
Spray a 9x13-inch pan with nonstick cooking spray.
Step 9
Make filling: Stir together brown sugar, cinnamon, ginger, and grated carrots in a small bowl.
Step 11
Roll dough into a rectangle that is about 12x15”. To fill, spread with melted butter and sprinkle with filling. Roll up lengthwise. Make roll as tight as possible. Cut into one-inch pieces. Place in greased pan so that rolls just touch each other. (You can slice it into 9-12 slices depending on how big you want your rolls.
Step 13
At this point you have two options: Let rise until doubled (about 20-30 minutes), then bake as directed below or Cover tightly with plastic wrap and chill overnight. Let the rolls come to room temperature before baking.
Step 15
Preheat oven to 350°F. Bake approximately 20-25 minutes.
Step 17
Make the frosting: beat cream cheese and butter until smooth, then mix in powdered sugar slowly. Mix until crumbly, then add vanilla and beat until smooth. Spread over warm or cooled rolls.
Step 19
Store loosely covered in refrigerator for up to 2 days. Rolls can be frozen before baking or after, or even after frosting.