Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, combine the creamy peanut butter, granulated sugar, and light brown sugar. Mix until smooth and creamy.
Add the egg and vanilla extract to the peanut butter mixture. Beat until fully incorporated.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the peanut butter mixture, mixing until just combined to form a dough.
Using a tablespoon, scoop dough and roll into balls. Place the dough balls 2 inches apart on the prepared baking sheets.
Flatten each dough ball slightly with the palm of your hand.
Bake for 10 to 12 minutes, or until the edges are lightly golden. Remove from oven and let cookies cool on the baking sheets for 5 minutes.
Transfer cookies to a wire rack to cool completely.
Once cooled, spread about 1 teaspoon of strawberry jelly on the flat side of half the cookies.
Top each jelly-spread cookie with another cookie, flat side down, to form sandwiches.
Serve immediately or store as directed.