1. Preheat oven to 180C/360F. Line baking sheet with parchment paper.
2. In a large mixing bowl cream together white sugar, brown sugar and butter until fluffy, about 3 minutes. Beat in the egg and vanilla extract, until combined. Mix in the peanut butter until smooth and creamy.
3. In a medium bowl stir flour, baking powder, baking soda and salt.
4. Add the flour mixture to the peanut butter mixture and beat until well combined. Place the batter in the refrigerator for 30 minutes.
5. Roll the batter into 1-inch (2.5 cm) balls. place the cookies on the baking sheet, leave about 2 inches (5 cm) apart. Flatten cookies, using a fork, in a crisscross pattern.
6. Bake the cookies for 10-12 minutes, or until lightly browned around the edges. Let cool 15-20 minutes.