Preheat oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, cream together peanut butter and butter until smooth.
Add both sugars and beat until light and fluffy, about 2-3 minutes.
Beat in egg and vanilla extract until well combined.
In a separate bowl, whisk together flour, baking soda, baking powder, and salt
Gradually add dry ingredients to the peanut butter mixture, mixing just until combined.
Form dough into 1-inch balls (about 1 tablespoon each) and roll in additional granulated sugar.
Place 2 inches apart on prepared baking sheets.
Using a fork, press a criss-cross pattern on top of each cookie, flattening slightly.
Bake for 10-12 minutes until edges are set but centers still look slightly underdone.
Allow to cool on baking sheets for 5 minutes, then transfer to wire racks to cool completely.