Preheat the oven to 350°F. Spray 2 (8-inch) round springform cake pans with cooking spray.
In a small bowl, prepare the flax eggs by whisking together the ground flax and water. Set aside for at least 10 minutes.
In a separate medium bowl, mix the coconut milk and vinegar. Whisk and set aside.
In a large bowl or stand mixer, mix the almond flour, brown rice flour, coconut sugar, raw cacao powder or cocoa powder, baking powder, baking soda, and salt. Stir to blend.
To the bowl with the coconut milk and vinegar, add the flax eggs, pumpkin puree (or avocado or banana), coconut nectar or maple syrup, and vanilla. Blend until creamy.
Pour the wet ingredients into the bowl with the flour mixture and start beating on medium speed. Incorporate the melted coconut oil and continue to beat until a batter is formed, increasing the speed as needed. Mix the batter with a spatula to work everything together.
Evenly distribute the batter between the prepared cake pans, smoothing on top with a spatula until it reaches the sides. Bake for 30 to 35 minutes until a toothpick inserted in the center comes out clean or the internal temperature reaches between 200° and 210°F. Allow the cakes to completely cool in the cake pans before frosting, about 2 hours.
Make the frosting. In a large bowl, mix the coconut oil and palm oil shortening. Beat with a hand mixer or immersion blender with the whisk tool until fluffy, about 1 minute.
Add the raw cacao powder or cocoa powder, arrowroot starch, coconut sugar, and salt and beat again. Add the coconut nectar or maple syrup and vanilla and beat until everything is combined, using a spatula to scrape down the sides as needed.
Using a spatula, mix the frosting. Frost the cooled cake immediately. Spread one-third of the frosting on top of one cake. Place the second cake on top and add the remaining frosting on top and around the sides.