Heat oven to 350° F. Butter an 8-inch square baking pan. Line the pan with a piece of parchment paper, leaving an overhang on 2 sides; butter the parchment.
In a medium bowl, whisk together the flour, baking powder, and salt; set aside.
In a large bowl, whisk together the butter, brown sugar, eggs, and vanilla until smooth. Add the flour mixture and mix until just combined (do not overmix). Fold in the peanut butter cups.
Spread the batter in the prepared pan and bake until a toothpick inserted in the center comes out clean, 40 to 45 minutes. Let cool completely in the pan. Holding the paper overhang, lift out the blondies. Cut into 16 squares.
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