Preheat oven to 350 degrees F. Line an 8 inch square metal pan with parchment or better yet, Release foil.
Thoroughly stir together flour, baking powder and salt. Set aside.
In a mixing bowl, beat together butter, peanut butter and both sugars. Beat in eggs and vanilla. Add flour mixture, stir until incorporated, then spread in pan.
Prepare chocolate swirl. Using microwave or double boiler, melt chocolate and butter. Drop by spoonfuls on top of peanut butter batter and drag a knife through the batter to marble.
Bake on center rack for 30-35 minutes or until edges appear brown and center appears set. I baked mine for 30 to avoid over-baking. Remove from oven and cool on a rack.
Meanwhile, prepare topping. Stir together peanut butter, vanilla and melted butter. Spread this mixture over the warm (not piping hot, not cool) brownies. Let cool completely.
Prepare Chocolate Swirl. Put chocolate in a heavy duty freezer bag. Microwave the bag for 30 seconds. Knead it with your hands to melt chocolate. Repeat, microwaving another 30 seconds and kneading bag, until chocolate is completely melted. Make sure there are no lumps. Snip a tiny hole in bottom corner of bag and drizzle chocolate decoratively over peanut butter.
At this point, it’s a good idea to chill the brownies to set the peanut butter and chocolate. I actually froze mine for about 20 minutes, then moved them to the refrigerator. The point, again, is to set the topping so you can slice the brownies nicely.
When set, lift from pan and slice brownies in to squares or bars. If they're too firm to slice, let them sit at room temperature Let come to room temperature before eating. Store covered and at room temperature for softer brownies.
Makes 1 8 inch pan.