Banana Layer Cake with Caramel Cream and Pecans

Name: Banana Layer Cake with Caramel Cream and Pecans
Ingredients: 2 1/2 cups all purpose flour; 1 tablespoon baking powder; 1 /2 teaspoon (generous) fine sea salt; 3 /4 cup (1 1/2 sticks) unsalted butter, room temperature; 2 1/2 cups sugar, divided; 6 large eggs; 1 cup plus 2 tablespoons buttermilk; 2 small ripe bananas, peeled, cut into 1/4-inch cubes (about 1 1/2 cups); 1 1/2 cups (packed) golden brown sugar; 1 small ripe banana, peeled, cut into 1-inch pieces; 3 tablespoons unsalted butter, room temperature; 3 3/4 cups chilled heavy whipping cream, divided; 4 1/2 teaspoons fresh lime juice, divided; 4 1/2 teaspoons dark rum, divided; Sea Salt-Roasted Pecans (click for recipe)