Carrot Cake with Spiced Cream Cheese Frosting

Preheat the oven to 350°F with the rack in the center of the oven.
Begin by sifting flour, baking powder, baking soda, salt, and spices together into a medium bowl. Whisk all dry ingredients together until combined and set the bowl off to the side.
In the bowl of the stand mixer (or a large bowl if using a hand mixer), beat the eggs, granulated sugar, and brown sugar on medium speed using the paddle attachment until well combined and lightened in color (approximately 2 minutes). Decrease the speed to low and add the oil, melted butter, milk, vanilla extract, ginger, and orange zest until blended. Make sure to scrape down the sides of the bowl, if necessary, so that everything is fully incorporated.
Next, add the flour mixture in 3 additions (to avoid overmixing and getting flour all over your kitchen). Mix flour into batter until just incorporated. Lastly, mix in shredded carrots and pecans until blended.

Pour the batter evenly into two prepared 9-inch cake pans. It should be approximately 877g of batter in each cake pan. Place the cake pans in the oven and bake for 25-30 minutes (or until a toothpick inserted into the cake comes out clean). Cool the cake in the pans on wire racks for 15 minutes before inverting the cake pans onto the racks and removing the cake from the pans. Allow the cake to cool completely (i.e., to room temperature).

Start by sifting your powdered sugar in a medium sized bowl and set aside.
In the bowl of a stand mixer (or a large bowl if you are using a hand mixer), beat the cream cheese and butter at medium speed until smooth. Scrape down the sides of the bowl to incorporate all of the cream cheese.
Next, beat in the vanilla extract, ground cinnamon, ground ginger, ground nutmeg, and salt. Decrease the speed to low and add the sifted powdered sugar in three additions. Beat until combined after each addition. Increase the speed to high and beat until the frosting is light and creamy (approximately 2 minutes).
Use the frosting immediately on a room-temperature cake or store the frosting in an airtight container in the refrigerator for up to a week. If using the frosting from the fridge, allow it to come to room temperature so it spreads more easily.