Line an 8x8-inch baking pan with parchment paper, leaving the edges hanging over the sides. Preheat the oven to 350°F.
Beat the butter and sugar together until light and fluffy. Add in the egg and peanut butter and beat until smooth and creamy.
In a small bowl, mix together the flour, baking powder, and salt together. Pour the flour mixture into the butter mixture and mix until just combined. Press 3/4 of the dough into the bottom of the pan and press firmly.
Top with the jam and then drop pieces of the remaining dough on top of the jam.
Bake for 30-40 minutes, placing aluminum foil over the pan halfway through.
Allow to cool completely. Run a knife all along the edges of pan and use the edges of the parchment paper to life the bars out of the pan. Cut into small bars.
Best if stored in an airtight container for up to 5 days.