Preheat oven to 350 degrees.
In the bowl of a stand mixer, combine flour, baking powder, baking soda, cinnamon; set aside.
In a medium bowl combine the eggs, shredded carrots, brown sugar, sugar, oil and vanilla; mix until combined. Add carrot mixture to flour mixture, mix on low until just combined. Fold in 1/2 cup of the chopped walnuts. Do not over mix.
Pour batter into a greased 12x17 baking sheet; spread evenly. Bake for 20 minutes or until a toothpick inserted in the center comes out clean.
Cool completely and top with frosting (see directions below).
Using a mixer, cream together butter and cream cheese. Add the salt, vanilla and one cup of powdered sugar and mix until combined. Add remaining powdered sugar and mix until smooth and creamy.
If frosting is too thick for your liking, add some milk (around 1/2 - 1 TBS). Spread frosting over cooled cake.
Top cake with remaining chopped walnuts, cut cake into squares.