Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a large bowl, cream together the butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Using a cookie scoop or tablespoon, take a small portion of the dough and flatten it in your palm. Add a small spoonful of peanut butter and a small spoonful of jelly in the center, then fold the dough around the filling and roll it into a ball.
Place the dough balls on the prepared baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are golden brown. The centers may look slightly underbaked, but they will firm up as they cool. You might need to bake them in batches.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.