Preheat oven to 350 degrees Fahrenheit (175 degrees Celsius) and grease two 9-inch round cake pans.

In a medium bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, ginger, and nutmeg.

In a large bowl, whisk together vegetable oil, granulated sugar, and brown sugar until smooth.

Add eggs one at a time, whisking well after each addition, then stir in pumpkin puree and 1 teaspoon vanilla extract.

Gradually fold the dry ingredients into the wet ingredients until no streaks of flour remain.

Fold in the grated carrots until evenly distributed.

Divide the batter equally between the prepared cake pans.

Bake for 30 to 35 minutes or until a toothpick inserted into the center comes out clean.

Cool the cakes in the pans for 10 minutes, then invert onto wire racks to cool completely.

In a separate bowl, beat the softened cream cheese and butter together until light and fluffy.

Add the powdered sugar and remaining 1 teaspoon vanilla extract, beating until the frosting is smooth.

Frost the top of one cake layer, place the second layer on top, and frost the top and sides of the entire cake.