Step 1: Preheat your oven to 375°F (190°C). Line two baking sheets with parchment paper.
Step 2: In a large mixing bowl, cream together the softened unsalted butter, granulated sugar, and light brown sugar until the mixture is light and fluffy.
Step 3: Beat in the large egg and vanilla extract until they are well combined into the butter mixture.
Step 4: Add the creamy peanut butter to the bowl and mix until it is fully incorporated and smooth.
Step 5: In a separate medium bowl, whisk together the all-purpose flour, baking soda, and salt.
Step 6: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix the dough.
Step 7: Roll the cookie dough into 1-inch balls and place them about 2 inches apart on your prepared baking sheets.
Step 8: Using your thumb or the back of a small spoon, make a deep indentation in the center of each cookie dough ball.
Step 9: Bake the cookies for 6-7 minutes. Remove the baking sheets from the oven and carefully fill each indentation with approximately 1/2 to 1 teaspoon of your chosen jelly or jam.
Step 10: Return the cookies to the oven and continue baking for another 3-5 minutes, or until the edges are lightly golden and the jelly is bubbly.
Step 11: Let the cookies cool on the baking sheets for at least 5 minutes before carefully transferring them to a wire rack to cool completely.