Cream butter, peanut butter, and sugars in a large bowl till creamy. Beat in eggs.
Whisk together flour, baking powder, baking soda, and salt in a small bowl and stir into the wet ingredients just till combined.
Roll dough into balls and place on silicone lined or lightly greased cookie sheets. Flatten with a fork.
Bake at 375° for about 10 minutes.
Let sit on pans for 3-5 minutes, then remove to wire racks to cool.
Notes
If using crunchy peanut butter, I like to overfill the measuring cup a bit. Since the peanuts replace some of the peanut butter, I find that it helps keep the cookies moist.