Start by positioning the oven rack in the center. If you're baking right away, preheat the oven to 350°F (176°C). Line a baking sheet with parchment paper and set it aside for later.
In one bowl, whisk together the dry ingredients and set aside.
In a separate bowl, or the bowl of a stand mixer, combine the butter, sourdough starter, peanut butter, sugars, egg, and vanilla extract, mixing until well blended.
Add the dry ingredients to the wet mixture and mix until just incorporated. At this point, you can cover the bowl and refrigerate the dough for up to 3 days for a long ferment.
Using a cookie scoop or two spoons, portion out the dough and arrange each piece on the prepared baking sheet, fitting about 12 per sheet.
Dip the back of a fork in flour and press it into the top of each dough ball in a criss-cross pattern, gently flattening the mound into a disc shape as you go.
Finish by placing 1 teaspoon of jelly in the center of each cookie.
Bake for 11 to 13 minutes, or until golden brown.
Remove the tray from the oven and let the cookies rest on the baking sheet for 10 minutes.
Carefully move the baked cookies to a wire rack to finish cooling.
Once cooled, store them in an airtight container at room temperature for up to a week, or in a freezer-safe container in the freezer for up to 6 months.
