Beat the butter, peanut butter, granulated sugar, brown sugar and vanilla in a bowl with an electric mixer until smooth. Add the egg and beat until combined.
In a separate bowl, combine the oats, flour, baking soda, baking powder and salt. Add this to the butter mixture and mix until combined.
Roll the dough into tablespoon-sized balls and place them on baking sheets lined with parchment paper. Press down on each ball of dough to create a flat disk. Bake at 350F for 10 minutes, or until the edges are golden.