Preheat your oven to 350°F (175°C). Grease three 8-inch round cake pans and line their bottoms with parchment.
In a large bowl, combine flour, baking soda, and salt. In a separate bowl, blend sugar, 2 cups of mashed banana, oil, yogurt, buttermilk, vanilla, and eggs until smooth. Add this mixture to the dry ingredients, stirring until combined. Divide the batter equally among the pans.
Bake for 25-30 minutes in the preheated oven, or until a toothpick comes out clean. Let the cakes cool in the pans on a wire rack for 10 minutes, then remove them from the pans and allow them to cool completely, around 1 to 1 1/2 hours.
For the caramel sauce, combine sugar, cream, butter, cinnamon, and salt in a small saucepan. Cook over medium heat, whisking continuously until the butter is melted, and the sugar is dissolved, about 2 minutes. Whisk in 1 1/2 mashed banana, vanilla bean paste, and 3 tablespoons of rum, then remove from heat.
Place sliced bananas in a small bowl and drizzle with 4 tablespoons of caramel sauce and the remaining 1 tablespoon of rum; gently toss to coat. Let the remaining caramel sauce cool to room temperature, approximately 20 minutes.
To prepare the caramel frosting, beat butter in the bowl of a stand mixer fitted with the paddle attachment on medium speed until it becomes light in color, about 3 minutes. Gradually add powdered sugar and beat on medium speed for about 3 minutes until it turns light and fluffy. Add 1 cup of the salted banana caramel sauce and beat on low speed until combined, approximately 1 minute. Transfer 1 cup of frosting to a piping bag fitted with a #12 tip.
To assemble the cake, place one cake layer on a serving plate and spread with 2/3 cup of Caramel Frosting. Use the piping bag to create a ring of Caramel Frosting around the outer edge of the cake layer on top of the frosting.
Spoon half of the sliced banana mixture inside the frosting ring and spread it evenly. Top with the second cake layer.
Spread another 2/3 cup of caramel frosting over the second layer. Repeat the piping bag ring around the outer edge of the cake layer on top of the frosting.
Spoon the remaining sliced banana mixture inside the frosting ring and spread it evenly. Top with the remaining cake layer.
Spread the remaining frosting on the top and sides of the cake and smooth it out.
Use the piping bag to decorate as desired.
Slice and serve with the remaining 3/4 cup of caramel sauce.