Whisk together flour, baking powder, baking soda, and salt. Set aside.
Add peanut butter, softened butter, shortening, and brown sugar to the bowl of a stand mixer fitted with a paddle attachment. Mix on medium speed until light and fluffy, about 5 minutes—occasionally scraping down sides of bowl.
Add egg to mixer bowl. Resume mixing on medium speed just until smooth—occasionally scraping down sides of bowl.
With mixer on low, slowly stir in flour mixture until fully incorporated.
Cover and refrigerate about 2 hours or until firm.
Heat oven to 375°F.
Shape dough into 1¼-inch balls. Place about 3 inches apart on ungreased cookie sheet.
Flatten in crisscross pattern with fork dipped into sugar.
Bake 9 to 10 minutes or until light golden brown.
Cool 5 minutes; remove from cookie sheet. Cool on wire rack.