Preheat oven to 350° F. Grease an 8-inch square pan with butter and line with nonstick parchment paper, leaving a 2-inch overhang over edges.
Place butter and sugar in the bowl of an electric mixer fitted with the paddle attachment. A hand mixer may also be used. Beat on medium-high heat until fluffy, about 2 minutes. Add egg, peanut butter and vanilla, and beat for 2 additional minutes, until combined.
Whisk flour, salt and baking powder together. Add to moist ingredients and mix well.
Spoon 2/3 of mixture into prepared pan and spread evenly. Next, evenly spread jam on top of peanut butter mixture. Then, take small amounts of remaining dough and scatter randomly over top, trying to cover most of the surface. Sprinkle with chopped peanuts.
Bake approximately 30-40 minutes or until top is golden. Remove from oven and let cool completely before cutting. Cut into 16 squares.