Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a medium bowl, combine the peanut butter, egg, erythritol, baking soda, salt, and vanilla extract.
Mix all ingredients thoroughly until a smooth dough forms.
Using a tablespoon, scoop the dough onto the prepared baking sheet, spacing them about 2 inches apart.
Flatten each cookie slightly with the back of a fork, creating 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 to a wire rack to cool completely.