Preheat oven to 350 F. Butter and flour 2 9-inch springform pans. Set aside.
Sift together flour, 1 cup cocoa, baking powder, baking soda, salt, ancho, and 3/4 tablespoons orange zest. Add to bowl of stand mixer fitted with whisk attachment.
Add granulated sugar to bowl.
With mixer on speed 2, add almond milk, 1/2 cup butter, eggs, and 2 teaspoons vanilla.
In a small saucepan bring orange juice and orange liquor to a low boil. Add orange mixture to cake batter, whisking on speed 2. Raise level to speed 4 for 30 seconds.
Divide batter among cake pans and transfer to oven. Bake for 35 minutes. Allow cakes to cook in pans for 10 minutes, then remove from springform and allow to cool completely on wire rack.
Meanwhile, wash, dry and return bowl and whisk to stand mixer. In stand mixer add remaining cocoa, butter, and powdered sugar. Mix on speed 2 until thick, then increase to speed 4 slowly drizzling in whipping cream until frosting is light and fluffy. Add remaining orange zest to frosting and whip for another 20 seconds.
Place one layer of cake on a plate and top with 1/3 frosting. Spread into an even layer. Invert second cake layer and place on top of frosting. Top this layer with remaining frosting and spread around the top and sides of the cake.
Garnish with chocolate shavings.