Cream butter, peanut butter, and sugars in a large mixing bowl. Beat in egg, yolk, and vanilla extract.
Stir in flour, oats, baking powder, baking soda, salt, and both kinds of chips.
Scoop dough and roll into tablespoon sized balls, place on silicone lined or lightly greased cookie sheets. Flatten slightly with a cup or the palm of your hand.
Bake at 350° for about 9 minutes.
Let sit on the pans for about 5 minutes, then remove to cooling racks to cool completely.
Notes
I like to press additional white and peanut butter chips into the tops of the cookie dough balls before baking