Plantain Cake with Avocado Buttercream

Name: Plantain Cake with Avocado Buttercream
Ingredients: 2 cups superfine sugar; 2 3/4 cups cake flour; 1/2 teaspoon ground cinnamon; 1/2 teaspoon salt; 1 tablespoon baking powder; 1 cup warm milk; 1 very ripe plantain (mostly black); 1/2 cup unsalted butter; 1/4 cup shortening; 4 large eggs; 1 1/2 teaspoons vanilla extract; Avocado Buttercream, recipe follows; Plantain Chips, recipe follows; 1 cup unsalted butter; 7 cups powdered sugar, divided; 2 ripe avocados; 1 tablespoon vanilla extract; 1/4 teaspoon salt; 1 plantain; Sugar, as needed