Make the cake: Preheat the oven to 325 degrees F. Butter two 9-inch round cake pans and line the bottoms with parchment paper. Butter the parchment and dust with cake flour, tapping out the excess; set aside.
Whisk the cake flour, almond flour, baking powder and salt in a separate large bowl; set aside. Beat the butter and granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 4 minutes. Beat in the eggs, one at a time, until incorporated, scraping down the sides of the bowl as needed. Beat in the vanilla and coconut extracts. Reduce the mixer speed to low; beat in the flour mixture in three additions, alternating with the milk. Increase the speed to medium high and beat until just combined.
Divide the batter between the prepared pans. Bake until the cakes are golden brown and a toothpick inserted into the centers comes out clean, 30 to 35 minutes. Transfer to a rack and let cool 10 minutes in the pans. Run a thin knife around the edges of the cakes and gently turn out onto the rack; remove the parchment and let cool completely.
Make the frosting: Put the chocolate in a microwave-safe bowl and microwave in 30-second intervals, stirring, until melted and smooth; let cool slightly. Combine the butter, confectioners' sugar, melted chocolate, cocoa powder, milk, rum and vanilla in a food processor. Pulse until smooth.
Place 1 cake layer on a serving plate and spread with 1 cup frosting. Top with the second cake layer, then frost the top and side of the cake with the remaining frosting. Sprinkle the top with the coconut.
Photograph by David Malosh