Prepare pans and oven. Adjust oven rack to middle position; heat oven to 350°F (177°C). Grease two 8 or 9-inch round pans) with nonstick cooking spray (or butter) and line with parchment paper on the bottom. Grease the parchment paper.
Combine dry ingredients. In a large mixing bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt in large bowl; set aside.
Grate carrots. Grate 6-7 medium carrots by hand. (if using food processor, use a large hole grater so it doesn't turn the carrots to mush). Set aside.
Combine wet ingredients. In a medium bowl, whisk together the oil, eggs, granulated sugar, and brown sugar until evenly combined.
Add dry ingredients. Stir in dry ingredients, with a spatula, just until no flour remains. Do not overmix. Fold in the carrots.
Bake. Divide the batter into prepared pans and bake until toothpick or skewer inserted into center of cake comes out clean, about 35 to 40 minutes, rotating pans halfway through baking time. Remove from the oven and allow to cool the cakes in the pan for about 10 minutes, then invert onto a cooling rack to continue cooling to room temperature in pan on wire rack, about 2 hours.
Make the cream cheese frosting. In a stand mixer with paddle attachment, or use a hand mixer in a large mixing bowl, cream together the butter and cream cheese until smooth and creamy. Add in the powdered sugar, 1/2 cup at a time, and beat to combine. Add in vanilla extract and beat to combine. Frost the cooled cake or store in the fridge for up to 5 days.