Pre-heat oven to 350°F and spray your 9x13-inch pan with baking spray. Line the length of the baking pan with parchment (optional). Skip the parchment if you plan to slice and frost the cake in the pan.
Peel and shred the carrots using the fine side of the box grater.
Separate the egg yolks from the whites and reserve both.
In a clean, dry, medium-sized bowl, whisk together the flour, baking powder, dry spices and salt. Set aside.
In a separate mixing bowl, beat the egg yolks and oil together on medium speed for 2 minutes. Add both sugars, vanilla extract, the juice from ½ of the orange and half of the orange zest. Continue to beat for 1 minute, then turn the mixer off.
Use a rubber spatula to fold the carrots and nuts into the wet mixture. Add the flour/dry ingredients and continue to fold until you can't see any streaks of flour.
Beat the egg whites on high speed in a clean mixing bowl with a clean whisk until they form frothy peaks (this takes about 2 minutes). If there are any traces of yolk in the bowl or on the whisk, the egg whites won't get stiff!
Fold the egg whites into the batter using a rubber spatula. The egg whites should be distributed evenly and the batter will look frothy. Pour the batter into the baking pan.
Bake the carrot cake for 40 minutes When your cake comes out of the oven, insert a toothpick in the center of the cake and if it comes out clean, it's done. The edges of the cake should feel soft when you press down gently on them.
Cool the cake fully in the pan or run a butter knife along the edges and flip it over to release it once fully cooled.