Preheat the oven to 350 degrees. Line a baking sheet with a silpat mat or parchment paper.
Combine the flour, baking soda, baking powder, and salt in a small bowl; mix well.
In a large bowl, cream the butter and peanut butter with a hand mixer, until combined.
Beat 1/2 cup of white sugar and the brown sugar until creamy and smooth.
Add the egg and vanilla. Beat until combined.
Slowly add the dry ingredients and mix with a rubber spatula, until just combined.
Make 2 tablespoon-sized balls of dough then roll them in the remaining 3 tablespoons of white sugar.
Place the cookies on the prepared baking sheet, about 2 inches apart.
Place in the oven to 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.