Preheat the oven to 350 degrees. Line a baking sheet with a silpat mat.
Combine together the flour, baking soda, baking powder, and salt in a small bowl; mix well.
In a large bowl, cream together the butter and peanut butter with a hand mixer, until combined. Add 1/2 cup of the white sugar and the brown sugar then beat until creamy and smooth. Add the egg and vanilla. Mix until combined.
Slowly add in the dry ingredients and mix with a spoon, until just combined.
Take about 2 tablespoons of dough and form it into a ball. Roll in the remaining 3 tablespoons of white sugar.
Place the cookies on the prepared baking sheet, about 2 inches apart.
Place into the oven and bake the cookies for 9-10 minutes or until they are golden at the edges and just set. Don't overbake!
Remove from the oven and let the cookies set on the baking sheet for 5 minutes before transferring them to a cooling rack. Serve with ice-cold milk. Enjoy.