Preheat oven to 300 degrees F (150 degrees C). Sift flour, baking soda, and salt together in a bowl.

Beat butter, creamy peanut butter, and crunchy peanut butter together in a large bowl until smooth. Beat egg white and white sugar into butter mixture until smooth. Add whole egg and brown sugar; continue to beat until smooth. Gradually stir flour mixture into butter mixture until batter is well mixed.

Roll the dough into 1 1/4-inch balls and place 2 inches apart onto ungreased baking sheets. Press balls with a fork creating a crosshatch. Freeze cookie dough on baking sheet until dough is firm, 5 to 8 minutes.

Bake in the preheated oven until cookies puff up, about 15 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.