Preheat oven to 350°F (conventional, no fan). Spray a 9x13 inch pan and line with parchment paper, leaving an overhang on two sides for easy removal.
Melt butter in a large heatproof bowl. Set aside to cool slightly while you measure the remaining ingredients.
Add sugar to the bowl and whisk vigorously until smooth. Whisk in the well-beaten eggs and extracts, beating very well until the mixture is smooth and slightly loosened.
Add flour, cocoa powder, baking powder, and salt. Whisk until no lumps remain. Sift the cocoa powder first if it is lumpy.
Pour the batter into the prepared pan. Dot peanut butter in random spots across the surface, then drag a thin offset spatula, knife, or wooden skewer through it in swirling motions to ribbon it through the batter. Work quickly before the surface begins to set.
Bake 22 to 25 minutes, until the center puffs slightly and jiggles like Jello when the pan is gently shaken. Cool completely in the pan.
For clean slices, cool to room temperature, wrap the pan, and refrigerate for at least 2 hours. Slice with a large, sharp chef's knife.
Notes
Doneness cue: The center should puff slightly and jiggle like Jello when the pan is shaken. The brownies will continue to set as they cool. Coffee extract: If you do not have it, omit it or replace with an equal amount of vanilla extract. You can also add 1 tablespoon of instant espresso powder to the dry ingredients. Storage: Store cooled, sliced brownies wrapped in plastic wrap or in an airtight container. They will keep soft and chewy for 1 week at room temperature, up to 2 weeks refrigerated, or up to 2 months frozen. Once sealed, the edges will lose their slight crunch.