Preheat your oven to 350°F (175°C) and line a large baking sheet with parchment paper.
In a medium mixing bowl, combine the creamy peanut butter, granulated sugar, egg, vanilla extract, baking soda, and salt. Mix with a wooden spoon or an electric mixer on low speed until a uniform, slightly sticky dough forms.
Using a 1-tablespoon cookie scoop or a spoon, portion the dough and roll it between your palms to form 1-inch balls. Place the dough balls about 2 inches apart on the prepared baking sheet.
Use the tines of a fork to gently press down on each dough ball, creating a classic criss-cross pattern. Press just until the dough is about 1/2-inch thick.
Bake for 10 to 12 minutes, or until the edges are set and lightly golden. The centers will still look soft.
Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely. They will firm up as they cool.