In a medium bowl, whisk together flour, baking powder, baking soda, and salt; set aside.
In a large bowl, using an electric hand mixer, beat peanut butter and butter on medium speed until smooth. Add granulated and brown sugar, beat until light and fluffy. Add the egg and vanilla, beat until well combined. Reduce speed to low and gradually add dry ingredients, beat until well incorporated. Cover the bowl and refrigerate for 1 hour.
Preheat oven to 350 degrees. Line 3 baking sheets with parchment paper; set aside.
Scoop level tablespoons of dough and roll into balls. Roll each ball in granulated sugar, and transfer to prepared baking sheets, spacing about 2 inches apart.
Bake cookies for 10 minutes. Remove from the oven. Using back of a 1/2 teaspoon or your thumb, make rounded indentation in top of each cookie. Return to oven, and bake until edges are golden, about 5-6 minutes more. Transfer sheets to wire racks, and let cool completely.
Heat jam in a small microwaveable bowl for 15 seconds; stir until smooth. Spoon about 1/2 teaspoon into each indentation.
Cookies can be stored in a single layer for up to 1 week.