Preheat oven to 350° Fahrenheit. Adjust oven racks as needed so cake pans will sit in center of oven.
Cut parchment paper to fit inside cake pans (see Notes below), then grease bottom and sides of each cake pan with cooking spray, ghee, or coconut oil. Fit parchment paper circle in bottom of each cake pan and set pans aside.
Crack eggs directly into large mixing bowl. Whisk eggs well until just combined, being careful not to over-whisk.
Add coconut sugar, coconut oil, and vanilla extract to egg mixture. Whisk until ingredients are just combined.
Add crushed pineapple, grated carrots, almond flour, coconut flour, tapioca flour, baking soda, salt, cinnamon, and ginger to bowl. Continue whisking until ingredients are well combined and batter is thick and mostly smooth. Be careful not to over-mix.
When batter ingredients are fully incorporated, add chopped pecans to mixture. Gently fold in pecans until just distributed.
Transfer cake batter into prepared cake pans, making sure to fill cake pans evenly.
Place filled cake pans in preheated oven. Bake cake layers 20 minutes. Note: if 3 cake pans won't fit on one oven rack, split pans between 2 racks. Bake 10 minutes, then rotate pans and bake 10 minutes more.
After 20 minutes, begin testing doneness of cake layers. Insert toothpick into center of each cake layer, then quickly remove toothpick. If toothpick does not come out of cake with very few crumbs, continue baking cake layers, checking doneness every 1 to 2 minutes.
Once toothpick can be removed from cake covered in few crumbs, remove cake pans from oven and set aside. Allow cake layers to rest in cake pans until layers are completely cool.