Preheat oven to 350 degrees. In a large mixing bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.

In a stand mixer or large mixing bowl with a hand mixer, beat the peanut butter and butter at medium speed until smooth. Add sugars, and beat until fluffy. Add egg and vanilla, and beat until combined. Reduce speed to low, then add dry ingredients, and mix until just combined.

Scoop level tablespoons of dough, roll into balls, then roll each ball in granulated sugar. Arrange the cookies 2 inches apart on parchment lined baking sheets.

Bake for 10 minutes, then remove the under baked cookies from oven to make an indentation in centers by pressing with the handle end of a wooden spoon. Return to oven, and bake until edges are golden, 6 to 7 minutes more. Transfer sheets to wire racks, and let cool completely.

In a small microwave safe bowl, microwave the jam on high for 45 seconds, or until loosened and easy to spoon. Spoon 1/2 teaspoon of jam into each cookie indentation.

Will keep in an airtight container for 1 week.