Preheat the oven to 350°F. Lightly grease two 9-inch round cake pans with baking spray or butter, and line the bottoms with parchment paper.

In a large mixing bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.

In a separate medium bowl, whisk together the sugars, oil, eggs, and vanilla until well combined. Pour the wet ingredients into the dry mixture and stir together just until combined and only a few streaks of flour remain.

Fold the carrots and pecans into the batter. Divide the batter evenly into the prepared pans.

Bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake layers to cool completely in the pans set on a wire cooling rack. Once cooled, invert the layers and remove the parchment paper.

In a large mixing bowl with a hand mixer or a stand mixer fitted with the paddle attachment, beat the butter on medium speed until very soft and smooth, about 1 minute. Add the cream cheese and beat until fluffy, about 30 seconds.

With the mixer on low speed, gradually add in the powdered sugar. (Use more sugar for a firmer, sweeter frosting.) Once combined, scrap down the bowl and add the vanilla. Beat on medium-low speed until fluffy and easily spreadable, about 1 minute.

Place one cooled cake layer top-side up on a cake stand or serving platter and spread ¾ cup of frosting over the top, all the way to the edge of the cake. Place the other cake layer top-side down on top. Spread the remaining frosting over the top and side of the cake.

If you desired, you can save some of the frosting to pipe decorations onto the cake or press chopped toasted pecans onto the frosting. Chill the cake for 30 minutes to set the frosting before slicing. Keep leftovers covered and refrigerated for up to 1 week.