Steps

1. Preheat the oven to 350 °F.
2. Toast the walnuts about 7 minutes, until they smell fragrant and are only lightly toasted. Cool.
3. Butter the inside of three 9-inch round cake pans. Line each with a round of wax paper. Butter and flour the round.
4. Grate the carrots into fine shreds, easiest done with the shredding attachment of a food processor. This should yield about 4 cups packed. Transfer to a large mixing bowl.
5. Beat the sugar, eggs, and vanilla extract until thickened, easiest in the now-empty food processor with the steel blade. Beat in the oil gradually until emulsified.
6. Sift together the flour, baking powder, baking soda, cinnamon, and salt.
7. Stir the dry ingredients into the egg mixture, or add to the food processor and process briefly until incorporated. Fold in the carrots and walnuts just until blended.
8. Distribute the batter among the three cake pans. Bake 35 to 40 minutes, until the tops spring back when gently pressed.
9. Remove from the pans and cool on a wire rack. Fill and frost with Cream Cheese Frosting.