Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, combine the natural peanut butter and erythritol. Mix well until smooth.
Add the 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 the dough and roll it into balls. Place the balls on the prepared baking sheet about 2 inches apart.
Flatten each ball gently with a fork, creating a crisscross pattern on top of each cookie.
Bake in the preheated oven for 10 to 12 minutes, 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.