Set oven temperature to 350°F. Grease two 9-inch circular cake pans lightly with butter or baking spray, then cover the bottoms with parchment paper.

Mix the flour, baking soda, baking powder, salt, cinnamon, and nutmeg in a large mixing basin.

Beat the sugars, oil, eggs, and vanilla well in a different medium-sized dish. After adding the wet ingredients to the dry mixture, stir only until everything is well blended and there are no more flour streaks.

Mix the pecans and carrots into the batter. Evenly distribute the batter among the ready pans.

When a toothpick put into the center comes out clean, bake for 30 to 35 minutes. Let the cake layers cool fully in the pans placed on a cooling rack made of wire. Turn the layers over and take off the parchment paper when they have cooled.

Using a hand mixer or a stand mixer with a paddle attachment, beat the butter in a large mixing bowl on medium speed for approximately one minute, or until it is very soft and smooth. After adding the cream cheese, beat for 30 seconds or until frothy.

Add the powdered sugar gradually while running the mixer on low speed. (If you want a stiffer, sweeter frosting, use more sugar.) After mixing, add the vanilla and scrape down the bowl. Beat for approximately a minute at a medium-low speed, or until fluffy and spreadable.

Using a cake stand or serving dish, place one cooled cake layer top-side up and cover with ¾ cup of frosting, extending all the way to the cake's edge. Top with the remaining cake layer, top side down. Cover the cake's sides and top with the leftover icing.

If preferred, you may press chopped toasted nuts over the frosting or reserve some of the frosting to pipe embellishments onto the cake. Before slicing, let the cake cool for thirty minutes to solidify the frosting. Store leftovers in the refrigerator for up to a week, covered.