Beat the butter until creamy, 2 minutes. Add the brown sugar and white sugar, beat for 2 more minutes. Mix in the peanut butter and the egg.
In a separate bowl, vigorously whisk together the dry ingredients—the flour, baking soda, baking powder and salt. Stir the dry ingredients into the sugar butter mixture.
Wrap dough in plastic and refrigerate at least 3 hours.
Preheat the oven to 375°F (190°C).
Shape the dough into 1 ¼ inch balls. Place the balls of dough about 3 inches apart on ungreased cookie sheets. Flatten in a crisscross pattern with a fork.
Bake one sheet at time on the center rack at 375°F (190°C) until light brown, about 9 to 11 minutes. Remove the cookies from the oven and let cool in their baking sheets for a minute. After 1 minute, transfer the cookies to a rack to cool completely.
