Preheat the oven to 350°F. Grease and line an 8x8-inch square baking pan with parchment paper, leaving some overhang for easy removal.
In a microwave-safe bowl, combine the coarsely chopped dark chocolate and butter. Microwave in 30-second intervals, stirring well after each interval, until the chocolate and butter are completely melted and smooth.
Add the granulated sugar to the melted chocolate mixture and stir until well combined. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the flour, cocoa powder, and salt.
Gradually add the dry ingredients to the chocolate mixture, stirring until just combined. Be careful not to overmix. Pour the batter into the prepared baking pan and spread it evenly.
Warm the peanut butter in the microwave for about 20-30 seconds until it becomes slightly runny. Drizzle the warm peanut butter over the brownie batter in a swirling motion. Use a knife or toothpick to gently swirl the peanut butter into the batter, creating a marbled effect.
Transfer the pan to the oven and bake for 25-30 minutes or until a toothpick inserted into the center of the brownies comes out clean.
Remove the pan from the oven and allow the brownies to cool completely in the pan on a wire rack. Once cooled, lift the brownies out of the pan using the parchment paper overhang. Cut into squares and serve.