Preheat oven to 350°F and fill cupcake pans with 18 cupcake liners.
In a large bowl, whisk together the sugars and oil. Add the eggs, vanilla, sour cream, and applesauce - mixing after each addition.
In a separate bowl, whisk together the flour, baking powder, baking soda, salt, and spices. Sift the dry ingredients into the wet ingredients and gently mix with a spatula until only a couple of flour streaks are visible.
Fold the shredded carrots into the batter.
Fill cupcake liners ~⅔ full and bake one pan at a time for about 20 minutes, or until a toothpick inserted in the middle of one comes out clean. After 10 minutes, move the cupcakes from the pan to a cooling rack.
Cream Cheese Frosting
Place the butter in a pan over medium heat. Stir until the butter browns and gives off a nutty aroma. Let it cool.
Mix the cream cheese in a large bowl until smooth. Stir in the cooled brown butter, vanilla extract and powdered sugar. Mix very well.
Pipe or spread frosting on the cooled cupcakes. Enjoy!
Accurate Measurements: Use a food scale to weigh the flour in grams (see metric tab). If using measuring cups, spoon the flour into the cups and level it off with a straightedge (do not pack it).Storage: Store unfrosted cupcakes at room temperature for up to 3 days or wrapped in the freezer for up to 1 month. Store frosted cupcakes in the refrigerator for up to 1 week.Nutrition: The provided nutrition information is an estimate, the calorie accuracy is not guaranteed.