Preheat oven to 350° F. Grease a 9-in by 9-in square baking pan, set aside.
Place the chocolate and butter in a microwave-safe bowl. Heat until melted, stirring to combine. (Be careful not to overheat.) Set aside.
In a mixer bowl fitted with the paddle attachment, mix together the eggs and sugars until well combined, about 2 min. Add in the vanilla. Next, add in the slightly cooled chocolate-butter mixture, mix just until incorporated.
Add the flour and salt, mixing until just combined. Pour the batter into the prepared pan, spread until even. Drop small amounts of the melted peanut butter around the top of the batter. With a butter knife, carefully swirl in the peanut butter into the brownie batter.
Bake for 20 to 25 minutes, or until a toothpick inserted into the center comes out clean. (Careful, the top of these brownies is a little sticky.)
Allow the brownies to cool completely before cutting them into pieces.
Notes
Semi-sweet chocolate chips can be a substitute for the chopped semi-sweet chocolate.