Step 1: Preheat your oven to 350°F (175°C) and grease an 8×8 inch baking pan or line it with parchment paper leaving an overhang on two sides.
Step 2: In a large mixing bowl, combine the mashed bananas, melted butter, granulated sugar, and brown sugar. Whisk until well combined.
Step 3: Add the eggs and vanilla extract to the banana mixture. Whisk vigorously for about 1 minute until the batter looks smooth and slightly lightened in color.
Step 4: Sift the flour, cocoa powder, and salt directly into the wet ingredients. Using a rubber spatula, gently fold the dry ingredients into the batter until just combined. Do not overmix.
Step 5: Pour the batter into the prepared baking pan and spread it evenly into the corners.
Step 6: Drop spoonfuls of the warmed peanut butter onto the top of the brownie batter. Use a knife to gently swirl the peanut butter into the chocolate batter.
Step 7: Bake for 28-32 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs attached.
Step 8: Allow the brownies to cool completely in the pan before lifting them out and slicing into squares.