Preheat oven to 350 degrees F (175 degrees C).

Beat butter and peanut butter together in a bowl using an electric mixer until creamy and smooth; beat in brown sugar and white sugar until incorporated. Add egg and vanilla to creamed butter mixture and mix until smooth.

Whisk oats, flour, baking soda, baking powder, and salt together in a separate bowl; stir into creamed butter mixture until just incorporated. Carefully fold chocolate bars into dough. Drop dough by rounded teaspoonfuls onto ungreased baking sheets.

Bake in the preheated oven until edges are lightly browned, 8 to 10 minutes.