Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large bowl, combine the peanut butter, granulated sugar, and light brown sugar. Mix until smooth and creamy.
Add the egg and vanilla extract to the peanut butter mixture and beat until fully incorporated.
In a separate small bowl, whisk together the baking soda, salt, and all-purpose flour.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Roll the dough into 1-inch balls and place them 2 inches apart on the prepared baking sheets.
Using your thumb or the back of a teaspoon, make an indentation in the center of each dough ball.
Fill each indentation with about 1/2 teaspoon of strawberry jelly.
Bake the cookies for 10 to 12 minutes, or until the edges are lightly golden.
Remove from the oven and allow the cookies to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.