Preheat oven to 350 degrees F (175 degrees C). Line a 9×5-inch loaf pan baking parchment.
Stir almond flour, coconut flour, pumpkin pie spice, baking soda, baking powder, and kosher salt together in a bowl with a whisk to mix.
Beat pumpkin puree, eggs, maple syrup, coconut oil, and vanilla extract together in a separate bowl until smooth; add to the flour mixture and gently stir just until the dry ingredients are moistened. Pour the batter into the prepared loaf pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 55 to 70 minutes. Cool in the pan 15 to 20 minutes before removing to cool completely on a wire rack.