Preheat the oven to 350°F (175°C).
Grease and line a 9x13-inch baking pan with parchment paper.
Melt the butter in a medium saucepan over low heat.
Remove from heat and stir in the sugar, eggs, and vanilla extract until well combined.
Sift together the flour, cocoa powder, baking powder, and salt in a bowl. Then fold this mixture into the wet ingredients.
Add in the chocolate chips and fold them gently into the batter.
Pour half of the brownie batter into the prepared baking pan and smooth it out evenly.
In a separate bowl, warm the peanut butter and spoon it over the brownie layer. Use a knife to swirl it into the batter.
Pour the remaining brownie batter over the peanut butter swirl and smooth it out gently.
Bake for 25-30 minutes or until a toothpick comes out almost clean.
Let the brownies cool in the pan for at least 15 minutes before transferring them to a wire rack.
Cut into squares and enjoy your delicious fudgy peanut butter brownies!