1. Preheat oven to 350°F. Generously grease and flour a 9x13-inch baking pan; set aside.
2. In a medium bowl, combine 2½ cups flour, baking powder, salt, baking soda, 1¼ teaspoons cinnamon and nutmeg. In another medium bowl, whisk together eggs and 2 teaspoons vanilla.
3. In a large bowl using an electric mixer on low speed, beat together sugar and oil. Gradually add 1/3 of the flour mixture and 1/3 of the egg mixture; mix well. Continue adding flour and egg mixtures in alternating additions, mixing well; fold in carrots.
4. Pour batter into prepared pan and gently tap pan a few times against counter to work out any air bubbles. Bake for 45 minutes or until a toothpick inserted into the center comes out clean. Place cake on a wire rack and let cool completely.
5. In a large bowl using an electric mixer on medium speed, combine cream cheese, butter and 3 teaspoons vanilla; beat until just blended, scraping down sides of bowl. Reduce speed to low and add powdered sugar, in batches, beating until smooth before adding more; set aside.
6. Loosen sides of cooled cake with a sharp knife; invert onto a cooling rack to remove from pan. Gently tap bottom of pan if cake doesn’t immediately release.
7. Flip cake, right side up, and using a sharp serrated knife, cut cake lengthwise into 3 equal layers.
8. Spread 2 cups frosting on the first layer of the cake and top with another cake layer; repeat. Frost top of cake.
9. In a medium bowl, combine remaining flour and cinnamon, brown sugar, salt and walnuts. Stir in melted butter, then work it in with a fork until the texture resembles crumbs; sprinkle on top of cake.
10. Serve immediately or refrigerate until ready to serve. Store remaining cake in refrigerator for up to 5 days.
Nutrition Information Per Serving
Calories: 517 (Calories from Fat: 252); Total Fat: 28g (Saturated Fat: 11g); Protein: 5g; Total Carbohydrates: 65g (Dietary Fiber: 1g; Sugars: 51g); Cholesterol: 83mg; Sodium: 371mg