Add the butter, 1 cup of granulated sugar, and brown sugar to a mixing bowl and beat on medium speed until light and fluffy.
Beat in the peanut butter, eggs, and vanilla until smooth and combined, scraping down the sides of the bowl as needed.
Add the flour, baking powder, baking soda, and salt to the bowl and mix on low speed until the dough is fully combined.
Cover the bowl with plastic wrap and refrigerate for 1 hour.
After the dough has chilled, preheat the oven to 350 degrees. Line a baking sheet with parchment paper.
Use a large cookie scoop to scoop out the dough.
Flatten the dough into a patty and place about a teaspoon of jelly in the center of the dough. You may not use the full batch of jelly, depending on how heavily you fill the cookies. Carefully fold up the edges around the jelly. Completely seal the jelly in the dough. If needed, press small pieces of extra dough around any spaces where the jelly is peeking out. Roll the dough into a ball.
Place the remaining ½ cup of granulated sugar on a plate or in a shallow bowl and roll each cookie through the sugar to coat.
Arrange cookies on the prepared baking sheet, leaving space between the cookies for dough to spread. Don’t overcrowd the pan.
Bake for 13 minutes or lightly browned around the edges. Do not overbake.
Let cool for 15 minutes on the baking sheet before transferring to a wire rack to finish cooling.