Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a large mixing bowl, combine the creamy peanut butter and granulated sugar. Mix until smooth and creamy.
Add the large egg, baking soda, vanilla extract, and salt to the peanut butter mixture. Stir until all ingredients are fully incorporated and a dough forms.
Using a tablespoon, scoop out dough and roll into balls. Place the dough balls onto the prepared baking sheet about 2 inches apart.
Flatten each dough ball gently with a fork, creating a crisscross pattern on top.
Bake in the preheated oven for 10 to 12 minutes, or until the edges are lightly golden.
Remove the cookies from the oven and allow them to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.