Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a large mixing bowl, combine 1 cup creamy peanut butter and 1 cup granulated sugar. Mix until smooth.
Add 1 large egg and 1 teaspoon vanilla extract to the peanut butter mixture. Stir until fully combined.
Add 1/2 teaspoon baking soda and 1/4 teaspoon salt to the mixture. Stir until evenly incorporated.
Roll the dough into 1-inch balls and place them on the prepared baking sheet, spacing them about 2 inches apart.
Using a fork, gently press down on each ball to create a crisscross pattern.
Bake in the preheated oven 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 sheet for 5 minutes before transferring them to a wire rack to cool completely.