Preheat oven to 350°F with racks in upper and lower thirds.

Whisk together flour, baking powder, baking soda, and salt in a bowl.

Beat together butter, peanut butter, sugars, and oil with an electric mixer at high speed just until pale and creamy, about 2 minutes in a stand mixer or longer with a handheld. Add whole eggs, yolks, and vanilla and beat until just incorporated. Reduce speed to low, then add flour mixture in 3 batches, mixing until well incorporated.

Scoop scant 1/4cups of dough about 2 inches apart onto 2 ungreased large baking sheets. Flatten mounds with floured tines of a fork, making a crosshatch pattern, into 2 1/2-inch cookies (about 1/2 inch thick).

Bake, switching position of sheets halfway thorough baking, until slightly puffed and golden around edges, about 30 minutes total. Transfer cookies to racks to cool.

Switch an oven rack to middle position and make more cookies with remaining dough on a cooled baking sheet.