Prep: Heat oven to 350°F (175°C). Grease and line two 8-inch round pans or one 9x13-inch pan with parchment.
Lightly grease the parchment.
Mix dry ingredients: In a large bowl, whisk flour, baking powder, baking soda, salt, cinnamon, and nutmeg until evenly combined.
Mix wet ingredients: In another bowl, whisk brown sugar, granulated sugar, eggs, oil, yogurt, and vanilla until smooth and slightly thick.
Combine: Pour wet into dry. Stir with a spatula until just combined. Do not overmix.
Fold in carrots and mix-ins: Add grated carrots and any extras (pineapple, nuts, raisins).
Fold gently until evenly distributed.
Bake: Divide batter between pans. Bake 22–28 minutes for rounds or 30–35 minutes for a 9x13. The cake is done when the center springs back and a toothpick comes out with a few moist crumbs.
Cool: Let cakes cool in the pan 10 minutes, then transfer to a wire rack to cool completely before frosting.
Make frosting: Beat cream cheese and butter until fluffy.
Add powdered sugar, vanilla, and salt. Beat until smooth and spreadable.
Frost: For layers, spread frosting between the layers and over the top and sides. For a 9x13, frost the top generously.
Chill 15–20 minutes to set clean slices.