Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a large bowl, combine the peanut butter and granulated sugar. Mix until smooth.
Add the egg, baking soda, vanilla extract, and salt to the peanut butter mixture. Stir until all ingredients are well combined.
Use a tablespoon to scoop dough and roll into balls. Place the balls on the prepared baking sheet about 2 inches apart.
Flatten each ball gently with a fork, making a crisscross pattern on top.
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 to a wire rack to cool completely.