Heat oven to 350 degrees F. Place nonstick aluminum foil in the bottom and overhanging sides of a 9 x 13 x 2-inch baking dish; set aside.
In a medium bowl, stir together flour, baking powder and salt until well blended.
Beat butter and sugar on medium-high speed until fluffy, about 2 minutes. Add egg and beat until incorporated. Add peanut butter and beat until well blended, about 2 minutes.
On low speed, add in flour and beat just until blended. Stir in vanilla extract. Spread into prepared pan and bake at 350 degrees F for 30 minutes. Remove from oven and spread with jam and sprinkle with peanuts; bake an additional 5 minutes. Cool completely on wire rack, then lift from pan using aluminum foil; cut into 18 bars.