In a medium bowl, whisk the egg and sugar together until thoroughly combined. Add the peanut butter and vanilla extract, and stir to combine. The batter will be thick at this point, now it is time to scoop.
Using a scant 1 tablespoon portion, drop the batter onto a parchment-lined baking sheet. Spray a small offset spatula with cooking spray and press the balls down until they are 1/3-inch thick; press a little more deeply in the center. Fill each with 1/4 teaspoon of the grape jelly and spread it in a thin layer.
Bake until golden brown, 15 to 18 minutes. Let the cookies cool; this part is really important, because it is when the cookies firm up and get their perfect cookie crunch.