Preheat oven to 350°F (175°C). Line a 9-inch square baking pan with parchment paper, and spray the lining with a nonstick cooking spray with flour. (Or skip the lining and grease the pan.)
Combine the cooled butter, sugar, brown sugar, eggs, and vanilla until thoroughly combined.
Add the flour and salt, and stir until combined.
Set aside 1/2 cup of the batter.
Add the melted chocolate to the remaining batter, stirring until combined.
Add the peanut butter to the reserved batter, stirring to combine.
Spread the chocolate mixture evenly into the bottom of the prepared pan. Dot the peanut butter mixture over the top of the chocolate layer, and then use a thin knife to swirl the batters together. Sprinkle with chocolate chips and/or chopped peanuts.
Bake for 20 to 25 minutes, or until a pick inserted into the center comes out clean or with a few moist crumbs.
Place the pan on a wire rack, and allow the brownies to cool completely before cutting into bars.
Notes
Store peanut butter swirl brownies in an airtight container at room temperature for 4 to 5 days. For longer storage, you can freeze the brownies for up to 3 months.