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Preheat oven to 325 degrees. Butter an 8-inch square baking pan and line with parchment, allowing a 2-inch overhang. Butter lining (not overhang).
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Make batter: Put butter and chocolates in a heatproof medium bowl set over a pan of simmering water; stir until melted. Let cool slightly. Whisk together flour, baking powder, and salt in a bowl.
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Whisk granulated sugar into chocolate mixture. Add eggs, and whisk until mixture is smooth. Stir in vanilla. Add flour mixture; stir until well incorporated.
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Make filling: Stir together butter, confectioners’ sugar, peanut butter, salt, and vanilla in a bowl until smooth.
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Pour one-third of batter into prepared pan; spread evenly with a rubber spatula. Drop dollops of peanut butter filling (about 1 tablespoon each) on top of batter, spacing about 1 inch apart. Drizzle remaining batter on top, and gently spread to fill pan. Drop dollops of remaining filling on top. Gently swirl peanut butter filling into batter with a butter knife, running the knife lengthwise and crosswise through layers.
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Bake until a toothpick inserted into brownies comes out with a few crumbs but is not wet, about 45 minutes. Let cool slightly in pan, about 15 minutes. Lift out; let cool completely on a wire rack before cutting into squares