Pre-heat the oven to 350 degrees. Butter a 9x13 baking dish.
In small saucepan over low heat, melt butter completely. Stir in sugar and continue cooking for 1-2 minutes, stirring constantly. Do not allow sugar mixture to boil.
Pour butter mixture into a large bowl or stand mixer, beat in cocoa powder, eggs, salt, baking powder, espresso powder, and vanilla extract. Mix until well combined.
Stir in the flour until well combined.
Spread the batter into prepared pan (it will be very thick and sticky).
To make the peanut butter swirl:
Stir together all of the ingredients in a small bowl until well combined.
Drop large spoonfuls of the filling over the brownie batter.
Use a butter knife to swirl the mixture into the brownie batter.
Bake for 30-35 minutes or until a tester comes out mostly clean.