Preheat oven to 350 degrees Fahrenheit. Line 24 muffin cups with paper liners.

Stir together flour, baking powder, baking soda, and salt in a small bowl.

In a large bowl, beat together brown sugar, peanut butter, applesauce, oil, and vanilla with an electric mixer until smooth and well combined. Add eggs, one at a time, beating after each addition until combined. Beat in flour mixture, alternating with buttermilk, on low speed until just combined.

Fill prepared muffin cups 2/3 full. Bake until a toothpick inserted in centers comes out clean, 14 to 16 minutes. Let cupcakes cool in muffin cups 5 minutes. Using a knife loosen edges; carefully remove cupcakes and transfer to a wire rack to cool completely. Frost.

To make banana butter frosting; beat one cup mashed banana, one teaspoon lemon juice, in 1/4 teaspoon salt in a large bowl with an electric mixer on medium speed 30 seconds. Beat in 1/2 cup softened butter until creamy, about 1 minute. Slowly beat in 7 cups of powdered sugar, one at a time, until smooth. Makes 4 cups.