Preheat oven to 350°F (175°C) and grease an 8x8 inch baking pan or line with parchment paper.
In a large bowl, cream together softened butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the egg, peanut butter, and vanilla extract until well combined.
Whisk together flour, baking powder, and salt in a separate bowl; gradually stir into the peanut butter mixture.
Fold in the rolled oats until evenly distributed.
Press approximately two-thirds of the dough into the bottom of the prepared baking pan.
Spread the preserves evenly over the dough layer.
Crumble the remaining dough over the top of the preserves.
Bake for 30 minutes or until the top is golden brown.
Allow bars to cool completely in the pan before cutting into squares.