Preheat the oven to 320°F/160°c. Line a 9-inch/20cm square baking tin with baking parchment, or spray with non-stick cooking spray. Set aside.
Add the butter and semi-sweet chocolate to a large microwave safe mixing bowl. Microwave in 30 second bursts, stirring in between, until melted and smooth.
Add the granulated sugar, eggs and vanilla extract to the chocolate mixture. Whisk until well combined.
Add the all-purpose flour, cocoa powder and salt to the batter, and whisk until just combined.
Pour half of the brownie batter into the baking tin and smooth the surface. Spoon over ¾ cup of the peanut butter. Top with the remaining brownie batter and gently smooth the surface, trying not to disturb the peanut butter blobs underneath.
Spoon over the remaining peanut butter. Swirl gently over the surface of the batter with a knife or skewer.
Bake the brownie for 30–35 minutes, or until the edges have just set, and the center is still soft. Allow to cool in the tin before removing and slicing (unless serving warm).