Preheat oven to 375°F (190°C) and line a standard 12-cup muffin tin with paper liners.
In a large bowl, whisk together the mashed bananas, granulated sugar, brown sugar, egg, melted butter, and vanilla extract until emulsified.
In a separate bowl, whisk the flour, baking soda, baking powder, and salt to ensure even distribution of leavening agents.
Gently fold the dry ingredients into the wet mixture using a spatula until no dry streaks remains; do not overmix.
Drop 1/4 cup of the creamy peanut butter into the batter and fold twice to create thick swirls.
Distribute half of the batter evenly across the 12 muffin cups.
Place 1 teaspoon of jelly and 1 teaspoon of the remaining peanut butter into the center of each muffin cup.
Top with the remaining batter, ensuring the jelly and peanut butter centers are covered.
Bake for 18 to 20 minutes, or until a toothpick inserted into the cake portion comes out clean.
Allow muffins to cool in the tin for 5 minutes before transferring to a wire rack for final cooling.