Preheat your oven for 350 degrees. Grease an 8x8 or 9x9 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 and fluffy.
Turn the mixer on low and add in the egg, vanilla, and peanut butter just until combined.
In a small bowl, sift together the flour, baking powder, and salt. Slowly add the flour mixture to the peanut butter mixture with the mixer on low just until combined.
Spread about 2/3 of the dough into the prepared pan and press into the bottom with your hands or an offset spatula.
Spread the jam evenly over the dough. Then with the remaining dough, drop small dollops over all of the jam.
Bake for 30-35 minutes, until golden brown.
Cool and cut into squares.