Preheat oven to 350°. Prepare muffin tins with paper liners (18 cups in all).
In a small bowl, whisk together flour, baking soda, baking powder, cinnamon, nutmeg, and salt; set aside.
In bowl of a standing mixer with a paddle attachment, beat together eggs, sugar, brown sugar, oil, milk, and vanilla on medium speed until light in color and thickened in texture, about 2 minutes.
Turn off motor. Add flour mixture and combine on low speed until just incorporated. Remove bowl from mixer and stir in carrots, raisins, and walnuts by hand.
Fill muffin cups two-thirds full. Bake cupcakes until brown and a toothpick inserted into the center comes out clean, about 25 minutes. When done, remove cupcakes from pan to a wire rack. Let cool to room temperature. When cool, top each cupcake with a tablespoon or more of Cream Cheese Frosting.
1 8-ounce package cream cheese
2 tablespoons unsalted butter, softened
1 cup confectioners’ sugar
1/2 teaspoon vanilla extract
In the bowl of a standing mixer with whisk attachment, combine all ingredients until smooth.