Prepare the Oven and Baking Pan: Preheat the oven to 350°F. Grease an 8 × 8-inch square baking pan and line it with parchment paper, leaving some overhang along the edges to make removing the brownies easier after baking.
Melt the Chocolate and Butter: Place the chopped dark chocolate and melted butter in a microwave-safe bowl. Microwave in 30-second intervals, stirring thoroughly after each interval, until both ingredients have melted completely and the mixture is smooth.
Incorporate the Sugar: Add the granulated sugar to the warm chocolate mixture. Stir until the sugar is evenly incorporated and the mixture is well combined.
Add the Eggs and Vanilla: Mix in the eggs one at a time, stirring well after each addition. Add the vanilla extract and stir until evenly distributed throughout the chocolate mixture.
Combine the Dry Ingredients: In a separate bowl, whisk together the all-purpose flour, unsweetened cocoa powder, and salt until the ingredients are evenly mixed.
Prepare the Brownie Batter: Gradually add the dry ingredient mixture to the chocolate mixture. Stir gently until the ingredients are just combined and no dry pockets remain, taking care not to overmix the batter.
Fill the Baking Pan: Transfer the brownie batter to the prepared baking pan. Use a spatula to spread it evenly into the corners and across the surface.
Warm the Peanut Butter: Place the creamy peanut butter in a microwave-safe bowl and microwave for 20–30 seconds, or until it becomes slightly runny and easy to drizzle.
Create the Peanut Butter Swirl: Drizzle the warmed peanut butter over the brownie batter in a swirling pattern. Using a toothpick or knife, gently draw through the peanut butter and chocolate batter to create a marbled effect. Avoid mixing the two mixtures together completely so the swirls remain visible. Bake the Brownies: Place the pan in the preheated oven and bake for 25–30 minutes. Begin checking toward the lower end of the baking time. Insert a toothpick into the center of the brownies; they are ready when it comes out clean, according to the original recipe's doneness test. Cool the Brownies: Remove the pan from the oven and place it on a wire rack. Allow the brownies to cool completely in the pan so they can finish setting before being removed and sliced.
Slice and Serve: Once the brownies have cooled completely, use the parchment paper overhang to lift them out of the pan. Place them on a cutting surface, cut into 16 squares, and serve.