In a medium-sized bowl, whisk together flour, baking powder, and salt. Set aside.
In a large bowl using an electric mixer, cream together butter and sugars on medium speed; until light and fluffy. Add vanilla extract, peanut butter, and an egg; mix until combined.
Slowly add flour mixture to wet ingredients; mix just until combined.
Scoop dough into 2 teaspoon balls, or use a #60 disher to scoop balls of dough. Place dough on an ungreased baking sheet or silicone mat/parchment paper-lined baking sheet. Flatten dough balls with a fork in a criss-cross pattern.
Bake 10-12 minutes or until barely golden brown around the edges. Do not overbake. The tops will not brown. Cookies may appear to be soft and undone, but they will set as they cool.
Cool cookies on baking sheet for 5 minutes; transfer to a wire rack to cool completely. Eat & Enjoy!
Notes
Classic Peanut Butter Cookies should be stored in an airtight container and will keep 4+ days.