Preheat oven to 350°F. Lightly butter and flour three 6-inch round cake pans. Tap out any excess flour. Line cake pans with parchment paper and set aside.
In a large bowl, whisk together flour, cinnamon, nutmeg, baking soda, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, beat together coconut oil, brown sugar, and maple syrup until smooth. Scrape down bowl as needed. Add eggs one at a time, ensuring eggs are thoroughly incorporated. Add pumpkin puree and mix until combined. Batter may look curdled at this point.
Add flour mixture in two additions. Mix on low speed until there are no longer any dry streaks of flour. Scrape down bowl as needed.
Evenly distribute batter among prepared cake pans. Level batter as needed. Bake for 35-40 minutes until toothpick inserted in center of cake comes out clean. Allow cake to cool in pan for 10 minutes before unmolding. Remove cake from pan and allow to cool to room temperature on wire rack.