Prep your pans: Heat oven to 350°F (175°C). Line two 8-inch round cake pans with parchment and lightly grease the sides.
Mix dry ingredients: In a large bowl, whisk flour, granulated sugar, brown sugar, baking powder, baking soda, salt, cinnamon, and nutmeg until well combined.
Whisk wet ingredients: In another bowl, whisk eggs, oil, applesauce, and vanilla until smooth.
Combine: Pour wet into dry and stir just until no dry streaks remain.
Fold in grated carrots and any add-ins. Do not overmix.
Bake: Divide batter between pans. Bake 25–30 minutes, until the centers spring back and a toothpick comes out clean with a few moist crumbs.
Cool completely: Let cakes cool in pans 10 minutes, then transfer to a rack.
Cool fully before frosting.
Make frosting: Beat dairy-free butter and cream cheese until smooth. Add vanilla and salt. Beat in powdered sugar, starting with 3 cups, until fluffy and spreadable.
Assemble: Place the first layer on a plate, spread frosting on top, add the second layer, and frost the top and sides.
Chill 20 minutes to set if needed.