Preheat the oven to 350 degrees F (175 degrees C). Line a 9x9-inch baking pan with parchment paper.
Combine brown sugar, peanut butter, and butter in a large bowl. Beat with an electric mixer until smooth. Add egg and vanilla; beat until well combined.
Stir together rolled oats, oat flour, baking powder, and salt in a bowl. Gradually add oats mixture to the peanut butter mixture, mixing until just combined.
Press 2/3 of the dough evenly into the bottom of the prepared pan. Dollop jelly evenly over the dough, then sprinkle with peanut butter chips. Drop remaining dough over the top in small pieces.
Bake until lightly browned on top, 30 to 35 minutes. Cool in the pan on a wire rack for 1 hour before removing and cutting into bars.
