Preheat oven to 375 degrees.
Combine flour, baking soda, salt, cinnamon, allspice, and nutmeg. Set aside.
In a separate bowl, combine oil, white sugar, brown sugar, vanilla extract, and eggs. Mix until creamy. Fold in carrots, then add dry ingredients.
Divide batter among five 9-inch cake pans lined with parchment paper, and bake for 20–25 minutes. (Or, if using two pans, bake for 30–35 minutes.)
Remove from oven and cool on cooling racks.