Heat oven to 350°F. Line an 8-inch square pan with parchment, leaving overhang.
Stir peanut butter, powdered sugar, and heavy cream until smooth and thick; set aside.
Warm butter and chocolate in a saucepan on low, stirring until melted. Cool 5 minutes.
Whisk in granulated and brown sugars until glossy.
Whisk in beaten eggs and vanilla just until combined.
Sift flour, cocoa, salt, espresso powder, and baking powder over the bowl. Fold until no dry spots.
Spread batter evenly in the pan.
Dollop peanut butter mixture over batter. Swirl with a knife for marbled pockets.
Bake 24 to 28 minutes, until edges set and the center looks slightly fudgy.
Cool in pan, then chill 20 minutes for cleaner cuts. Lift, slice, and serve.