Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a large mixing bowl, combine 1 cup natural peanut butter and 1 cup granulated sugar. Mix well until smooth and creamy.
Add 1 large egg, 1 teaspoon baking soda, 1/2 teaspoon vanilla extract, and 1/4 teaspoon salt to the peanut butter mixture. Stir until all ingredients are fully incorporated and the dough is smooth.
Using a tablespoon, scoop out dough and roll into balls. Place the dough balls onto the prepared baking sheet, spacing them about 2 inches apart.
Flatten each dough ball slightly with a fork, creating a crisscross pattern on top of each cookie.
Bake in the preheated oven for 10 to 12 minutes, or until the edges are lightly golden but the centers remain soft.
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.