Prep the pans: Heat oven to 350°F (175°C). Grease and line two 8-inch round cake pans or one 9x13-inch pan with parchment.
Mix dry ingredients: In a large bowl, whisk flour, granulated sugar, brown sugar, baking powder, baking soda, cinnamon, nutmeg, and salt.
Whisk wet ingredients: In another bowl, whisk eggs, oil, applesauce, milk, and vanilla until smooth.
Combine: Pour wet into dry and stir just until blended. The batter will be thick.
Let it rest 5 minutes so the flour hydrates.
Fold in add-ins: Stir in carrots, pineapple (well-drained), nuts, and raisins if using.
Bake: Divide batter between pans. Bake 22–28 minutes for 8-inch rounds or 30–35 minutes for a 9x13, until a toothpick comes out with a few moist crumbs.
Cool completely: Let cakes cool in pans 10 minutes, then turn out to a rack. Cool fully before frosting.
Make frosting: Beat cream cheese and butter until creamy.
Add powdered sugar 1/2 cup at a time, then vanilla and salt. Beat until fluffy.
Frost: For rounds, spread frosting between layers and over the top and sides. For a sheet cake, frost the top generously.