Preheat oven to 325 degrees F. Prepare 2 9-inch cake pans: trace the bottom of each pan onto parchment paper, cut it out, and place in the bottom of the pan. Then generously spray the paper and the sides of the pans with nonstick spray.
In a large bowl or stand mixer, beat together white sugar, brown sugar, oil, Greek yogurt, vanilla, 4 eggs, and pineapple. (don't drain it!)
In a separate bowl, whisk together flour, (don't pack your flour! Spoon it into the measuring cup.), baking soda, baking powder, salt, cinnamon, and nutmeg.
Add dry ingredients to the wet ingredients and stir until combined.
Use a box grater to shred the carrots. It's annoying to do this by hand, but if you use a food processor, the shredded pieces will be too big and won't melt into the cake.
If you are adding pecans to the cake, toast the chopped pecans in a small skillet for a few minutes on medium until they start to smell good and are lightly browned.
Fold in the carrots and pecans.
Pour the batter into the prepared pans, do your best to distribute evenly. If you have a kitchen scale you can weigh them.
Bake at 325 for 38-40 minutes or until a toothpick comes out clean.
Wait about 20-30 minutes, then run a knife along the edge and flip the cakes onto cooking racks. Be careful! This cake is heavy but delicate. Eat as many crumbs and scraps and you can legitimately get your hands on.
Let cool completely.
At this point, you can either wrap your cakes in plastic wrap and freeze so that it is super easy to frost (that's what I did) or you can frost immediately. Just be careful.
For the frosting:
Chop up the pecans. You can chop them with a knife or in a food processor. Click on the photo of the frosting below the recipe to see what level of choppiness we're talking.
Set a frying pan over medium heat. Add the pecans and stir occasionally until they start to smell delicious, or until they barely start to brown. Set aside to cool.
In a large mixing bowl or stand mixer, cream the butter and cream cheese to within an inch of its life. Just kidding, beat it for a couple minutes until it's high and fluffy.
Add half the powdered sugar and all the maple syrup. Beat well.
Add the rest of the powdered sugar, maple extract, and salt. Beat well.
Add the chopped pecans when they are completely cooled and beat well.
Place one of the cake layers on your cake plate. Top with about 1 cup of frosting and spread. Top with the other cake. Frost the top and sides of the cake.
Garnish with toasted pecans.
*I haven't tried it, but using half applesauce and half oil is pretty common for carrot cake. Try it out to cut calories!