Heat the oven to 325°F. Spray the bottom and sides of an 8x8 glass baking dish and set aside.

Put the butter the chocolate in a large microwave-proof bowl and heat in 30-second bursts until the butter and chocolate have melted and can be stirred together until smooth. Working quickly, whisk in the sugar until the batter is smooth, then whisk in the eggs, and vanilla.

Combine the flour, baking powder, and salt in a small bowl and fold it into the brownie batter. Stir it until the flour is just incorporated and the batter is smooth. Then stop stirring so the batter does not get overworked.

Make the peanut butter filling by combine all of the filling ingredients in one bowl and stirring it until smooth and creamy.

Use a tablespoon to dollop the peanut butter mixture randomly top of the brownie in even amounts. Then, use a dull knife to swirl the peanut butter into the batter, running the knife horizontally through the peanut butter once or twice. Do not over-swirl the peanut butter or it will get too blended into the batter and disappear.

Bake the brownies for 40 to 45 minutes, or until a cake tester insert into the center comes out clean. Allow the brownies to cool completely in the pan, then cut into squares to serve.