Preheat the oven to 350 degrees F. Grease a 9x13 inch baking dish with nonstick spray.
In a bowl, whisk together the flour, coconut, baking powder, salt, soda, cinnamon, ginger, cardamom and allspice.
In a larger bowl, whisk together the eggs, coconut oil, sugars and pumpkin puree until smooth and combined. Stir in the vanilla extract.
Mix in the dry ingredients until they are all combined, being careful not to overmix. Spread the batter in the greased pan. Bake for 25 to 30 minutes, or until the center is no longer jiggy. Let cool completely before frosting.