How to Make It
Preheat oven to 425°F. Place bananas (in peel) on a parchment paper-lined baking sheet, and bake in preheated oven until peel is very dark and just starting to split open, 20 to 25 minutes. Let bananas cool completely, about 20 minutes. Remove and discard peels. Mash bananas in a small bowl to measure 1 1/2 cups. Save any remaining mashed bananas for another use or discard.
Reduce oven temperature to 350°F. Coat 2 (9-inch) round cake pans with baking spray. Beat 1/2 cup of the butter with a stand mixer fitted with paddle attachment on medium speed until creamy, 2 to 3 minutes, stopping to scrape down sides of bowl as needed. With mixer running on medium speed, gradually add brown sugar and granulated sugar, and beat until creamy, about 5 minutes, stopping to scrape down sides of bowl as needed. Add eggs, 1 at a time, beating until just combined after each addition. Beat in vanilla and 1 1/2 cups reserved mashed bananas on low speed until just combined.
Whisk together flour, baking powder, baking soda, cinnamon, and 1/2 teaspoon of the salt in a medium bowl. With mixer running on low speed and beating until just combined after addition, add flour mixture to banana mixture, alternately with buttermilk, beginning and ending with flour mixture. Pour batter evenly into prepared pans, and spread in an even layer.
Bake in preheated oven until a wooden pick inserted in center comes out clean, 23 to 28 minutes. Transfer pans to wire racks, and cool 10 minutes. Remove from pans, and cool completely on wire racks, about 1 hour.
Meanwhile, beat remaining 1 1/2 cups butter with stand mixer fitted with paddle attachment on medium speed until creamy, 1 to 2 minutes. Reduce speed to low; gradually add powdered sugar, rum, and remaining 1/4 teaspoon salt, and beat until smooth, about 2 minutes, stopping to scrape down sides of bowl as needed. Increase speed to medium, add 1 tablespoon of the cream, and beat until fluffy and spreadable, 1 to 2 minutes, adding remaining 1 tablespoon cream, 1 teaspoon at a time, if needed.
Spread frosting between layers and on top and sides of cake. Or, to decorate top of cake, spoon 1 cup of the frosting into a piping bag fitted with a No. 2D star tip before frosting cake. Spread remaining frosting between layers and on top and sides of cake. Pipe 12 stars around top edge of cake, and top each with a banana slice.