Preheat the oven to 350°. Line 18 cups of 2 standard 12-cup muffin pans with baking liners. In a large bowl, beat 1 stick butter with 1 cup granulated sugar until fluffy, about 4 minutes. Add 3/4 cup bananas, the baking powder and 1/2 teaspoon salt and beat until smooth. Stir in 1 cup flour. Mix in 6 tablespoons milk and the remaining 3/4 cup flour until smooth.
Using an electric mixer, beat the egg whites at medium speed until soft peaks form. Gradually mix in the remaining 1/4 cup granulated sugar at high speed until stiff and glossy. Fold the egg whites into the batter until no streaks remain.
Spoon the batter into the prepared muffin pans, filling each liner three-quarters full. Cut 9 caramels in half, and submerge one piece in each muffin cup of batter. Bake until the cupcakes are springy to the touch, about 25 minutes. Let cool.
Meanwhile, in a small, heavy saucepan, cook the remaining caramels, 1/4 cup milk, 1/4 cup banana and 1/4 teaspoon salt over medium heat, stirring, until the caramels are melted.
Using the electric mixer, beat the egg yolks and confectioners' sugar until thick, about 3 minutes. Slowly beat in the caramel mixture; transfer the mixture to the saucepan. Cook over medium-low heat, stirring constantly for about 1 minute. Transfer to a bowl and refrigerate until cool.
Using the electric mixer, beat the remaining 2 sticks butter at high speed until fluffy, about 5 minutes. With the mixer on low speed, slowly add the cooled caramel mixture, then beat at high speed until fluffy. Spread the frosting onto the cupcakes.