How to Make It
Preheat the oven to 350°. Butter two 9-inch round cake pans. Line the bottoms with rounds of wax paper and butter the paper. Dust the pans with flour, tapping out the excess.
In the bowl of a standing electric mixer fitted with a paddle, mix the flour, baking powder and salt. Add the shortening and mix at low speed until evenly blended. Add the sugar and mix at medium speed until a mass forms around the paddle. At low speed, gradually add 3/4 cup of the milk and beat until smooth, scraping down the side of the bowl from time to time.
In a medium bowl, whisk the egg whites with the remaining 3/4 cup of milk and the vanilla and almond extracts. With the machine on, gradually beat the egg white mixture into the batter at medium speed until silky, about 5 minutes. Scrape the batter into the prepared pans and bake for 30 to 35 minutes, until golden and springy. Transfer the cakes to a rack and let cool for 15 minutes in the pans, then invert them onto the rack and let cool completely. Peel off the wax paper and slice each cake in half horizontally.
In a large saucepan, cook the butter, brown sugar and cinnamon over moderately high heat until the butter and sugar have melted. Remove from the heat and add the bananas and 1/2 cup of the rum. Cook the filling over moderate heat, stirring frequently, until very thick and the butter just begins to separate, about 25 minutes.
Transfer the filling to a food processor. Add the remaining 2 tablespoons of rum and puree until smooth. Let the filling cool to room temperature, about 30 minutes.
In the bowl of a standing electric mixer fitted with a whisk, beat the butter at medium speed until creamy and fluffy, about 3 minutes. Add the confectioners' sugar and beat at low speed until incorporated. Add the vanilla and almond extracts and beat at medium-high speed until fluffy, about 3 minutes. Beat in the cream cheese until light and fluffy, about 3 minutes.
Place one cake layer on a large plate, and spoon one-third of the filling on top and spread it to the edge. Top with another cake layer, pressing gently; spread with another third of the filling. Repeat with the remaining cake layers and filling, ending with a cake layer. Spread the frosting over the top and side of the cake and refrigerate for at least 2 hours, or until set. Bring to room temperature before serving.