- Preheat oven to 350°F.
- Grease a 9-by-13-inch pan with butter, and line the bottom with parchment paper.
- Grease the parchment, and coat inside of pan with flour; set aside.
- Place butter and sugar in the bowl of an electric mixer fitted with the paddle attachment.
- Beat on medium-high speed until fluffy, about 2 minutes.
- On medium speed, add eggs and peanut butter; beat until combined, about 2 minutes.
- Sift together salt, baking powder, and flour.
- Add to bowl of mixer on low speed; combine.
- Add vanilla.
- Transfer two-thirds of mixture to prepared pan; spread evenly with offset spatula.
- Using offset spatula, spread jam on top of peanut-butter mixture.
- Dollop remaining third of peanut-butter mixture on top of jam.
- Sprinkle with peanuts.
- Bake until golden, about 45 minutes.
- Transfer to a wire rack to cool; cut into about thirty-six 1 1/2-by-2-inch pieces.
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