Preheat the oven to 350°F. Line the bottoms of two 9.5-inch cake pans with parchment paper and set the pans aside.
Measure 1 1/2 cups ripe avocado (scooped from peeled avocados) into a large bowl and mash until very smooth (use a fork, a potato masher, or a blender).
Add 6 large room-temperature eggs, 3/4 cup honey, 1 tablespoon vanilla extract, and 2 1/4 teaspoons pure peppermint extract to the mashed avocado. Beat with an electric hand mixer on high speed about 2 minutes, until the mixture begins to thicken and lighten in color.
Add the sifted 3/4 cup coconut flour (66 g), 3/4 cup tapioca flour (90 g), 3/4 teaspoon salt, and 2 tablespoons baking powder to the bowl. Stir until no dry streaks remain, then beat on medium speed until the batter is smooth.
Stir in 6 tablespoons (about 2 ounces) very finely chopped dark chocolate. Let the batter stand 10 minutes to allow the coconut flour to absorb moisture.
Divide the batter evenly between the two prepared pans and smooth the tops with a spatula.
Bake until the edges are lightly golden and a toothpick inserted into the center comes out clean, about 25 minutes. Remove the pans from the oven.
Let the cakes cool in the pans for about 10 minutes. Run a sharp knife around the edges, invert each cake onto a wire rack, remove the parchment, and let the cakes cool completely on the rack, about 15–20 minutes.
While the cakes cool, make the ganache: in a small saucepan whisk together 6 tablespoons full-fat coconut milk and 1 1/2 tablespoons honey. Heat over medium-high until the mixture is just about to boil (small bubbles at the edges and steam), but do not let it boil. Remove from heat.
Add 5 ounces roughly chopped dark chocolate to the hot coconut milk mixture. Let sit 30 seconds, then whisk until the chocolate is fully melted and the ganache is smooth and creamy.
Let the ganache sit at room temperature about 1 hour, until it thickens but remains pourable.
To assemble, place one cooled cake layer bottom-side up on a cake stand or plate. Pour a heaping 1/4 cup of ganache onto the center and spread it evenly over the top with a flat metal spatula.
Gently place the second cake layer bottom-side up on top of the ganache layer. Refrigerate the stacked cake about 15 minutes, until the ganache filling just sets.
Pour the remaining ganache over the top of the cake and spread it quickly, letting it drip down the sides and smoothing to coat the entire cake. Work promptly—the ganache will begin to firm up.
Let the ganache set briefly, then slice and serve. Enjoy.