Pour chestnuts (*see note) into a food processor or blender and pulse until very finely minced. It should be somewhere between the texture of flour and finely chopped nuts.

Preheat oven to 350 degrees F (180 C) and grease 3 8-in cake pans with oil and flour evenly. Stir vinegar and almond milk together in a measuring glass and set aside until needed.

Add the aquafaba to the bowl of a stand mixer fitted with a whisk attachment and turn on high speed to beat for about 5 minutes until beginning to look whipped and fluffy. Slowly add in the sugar while beating and continue beating for about 3 to 5 minutes longer until it forms stiff peaks.

In a separate mixing bowl, combine oil, milk/vinegar, salt, and vanilla and mix until smooth. Once the whipped mixture is full and fluffy, turn off mixer and remove bowl from stand. Sift in baking powder, chestnut "flour" and all purpose flour then fold lightly with a rubber spatula until just combined. Now add the liquid mixture and gently continue folding just until well incorporated into batter. Divide batter into pans as evenly as possible. Bake for 30 - 35 minutes until edges start to darken and a toothpick inserted in center comes out clean. Cool completely before frosting.

Beat butter (or organic shortening) in a large mixing bowl until creamed. Add vanilla, salt, nutmeg, and then powdered sugar one cup at a time. Add eggnog and beat until frosting is light and fluffy. Add more powdered sugar as needed for frosting to be a thick enough consistency.

To assemble, trim cakes until level, then spread frosting on one of the cakes and layer a second on top. Repeat frosting layer for next cake and place the third cake layer on top. Frost the top and all the sides with desired amount of remaining frosting until smooth (you'll probably have some extra frosting). You can use pastry bags and tips for edging and decorating.