Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper to ensure easy removal of the cookies.

In a large mixing bowl, combine the creamy peanut butter and granulated sugar. Mix until the ingredients are well incorporated and smooth.

Add the egg and vanilla extract to the peanut butter mixture. Stir until blended, then add the baking soda and salt. Mix until you have a uniform dough.

Using a tablespoon or cookie scoop, portion out the dough and roll it into balls. Place the balls on the prepared baking sheet, spacing them about 2 inches apart.

Flatten each dough ball slightly with the back of a fork, creating a crisscross pattern on top.

Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden. The centers may appear soft, but they will firm up as they cool.

Remove the cookies from the oven and let them cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely.