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Place the flour, baking powder, and salt in a small bowl and whisk to combine.
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Combine the butter and chopped chocolate in a medium microwave-safe bowl and microwave in 30-second intervals, stirring after each interval, until chocolate is melted and mixture is smooth. Let cool for 5 to 10 minutes, then stir in the sugar, eggs, vanilla, and espresso powder (if using). Stir in the dry ingredients until just incorporated.
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Warm the peanut butter in the microwave until it is liquid-y. Pour half of the brownie batter into the prepared pan. Drop dollops of filling over the batter and gently spread into an even layer; sprinkle the peanut butter chips over the top. Dollop the peanut butter over the filling mixture and use a knife to swirl the peanut butter into the filling. (Take care not to swirl it into the brownie batter.) Use an offset spatula to (gently) spread the remaining batter over the top of the filling.
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Bake 50 to 60 minutes, until a toothpick inserted into the center of the brownies comes out with just a few crumbs. Cool brownies in the pan set on a wire rack for at least 2 hours. Remove brownies from the pan using the excess foil, then slice into bars and serve.