Preheat oven to350˚F. Line the bottoms of 4(10 inch) cake pans with parchment paper. Set aside.
Place flour, baking powder, baking soda, cinnamon, salt, and nutmeg into a large mixing bowl and whisk together. In another mixing bowl combine butter, sugars, applesauce, eggs, and vanilla and whisk together.
Pour the wet mixture into the dry mixture ,in thirds, stirring together after each addition.
Continue to stir batter until completely combined and no dry spots remain. Fold in carrots and currants.
Fill each prepared cake pan evenly with batter.
Bake each cake round for 30 to 35 minutes or until a toothpick comes out clean when inserted into the center of each round.
Cool for 10 minutes before transferring each cake onto a cooling rack and cooling completely.Refrigerate cake layers for at least 2 hours.
For Frosting: With a stand mixer, fitted with a paddle attachment, beat together the cream cheese and butter until light and fluffy. Add powdered sugar, 1/2 cup at a time and continue to beat together. Add vanilla, scrape down sides of the bowl and continue to beat together for 1 minute.
To assemble: Slice off rounded cake tops to level them. Spread a thin layer of frosting between each layer of cake and neatly stack them atop one another. Frost the sides and top with a thin layer of frosting and refrigerate cake for an hour. Remove chilled cake from the refrigerator and add another layer of frosting. Add crushed walnuts to top (and sides, if desired). Slice and serve.
Makes 4 (8" round cake layers) **The recipe can be halved to make 1 (8"x 8") cake, with an increased bake time of 45-50 minutes.