Step 1: Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans or line them with parchment paper.
Step 2: In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt.
Step 3: In a large bowl, beat the sugar and vegetable oil together. Add the eggs one at a time, beating well after each addition. Stir in 1 teaspoon of vanilla extract.
Step 4: Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Do not overmix.
Step 5: Fold in the grated carrots and chopped walnuts gently using a spatula.
Step 6: Divide the batter evenly between the prepared pans and bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Step 7: Allow the cakes to cool in the pans for 10 minutes, then turn them out onto wire racks to cool completely.
Step 8: To make the frosting, beat the cream cheese and butter together until smooth. Add the powdered sugar and 1 teaspoon of vanilla, and beat until light and fluffy.
Step 9: Once the cakes are completely cool, frost the top of one layer, place the second layer on top, and frost the top and sides of the entire cake.