Assemble ingredients and tools. Preheat the oven to 350 degrees. Grease a 9 x 5-inch loaf pan.
In a medium bowl, whisk together the flours, baking soda and spices.
Grate the carrot and set aside.
In the bowl of your electric mixer, cream together the butter and sugars. Beat in the eggs and vanilla, scraping down the sides as needed.
Beat in the applesauce.
Add the dry ingredients and mix on low until just combined. Fold in the grated carrots.
Spread the batter evenly in the prepared pan.
Bake until a toothpick comes out clean. About 55-65 minutes. Let the bread cool in the pan on a rack for 10 minutes, then remove from the pan to the rack. Allow the bread to cool completely before slicing.