Preheat the oven to 350 degrees F.
Grease a 9 by 13 by 2-inch cake pan. Line it with parchment paper, then grease and flour the pan.
In the bowl of an electric mixer fitted with the paddle attachment, cream the butter and sugar on medium speed until light yellow, about 2 minutes. With the mixer on low speed, add the vanilla, eggs, and peanut butter and mix until all ingredients are combined.
In a small bowl, sift together the flour, baking powder, and salt. With the mixer on low speed, slowly add the flour mixture to the peanut butter mixture. Mix just until combined.
Spread 2/3 of the dough into the prepared cake pan and spread over the bottom with a knife or offset spatula. Spread the jam evenly over the dough. Drop small globs of the remaining dough evenly over the jam. Don't worry if all the jam isn't covered; it will spread in the oven. Sprinkle with chopped peanuts and bake for 45 minutes, until golden brown. Cool and cut into squares.