Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a large mixing bowl, combine 1 cup creamy peanut butter and 1 cup granulated sugar. Mix 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 well incorporated and form a dough.
Using a tablespoon, scoop out dough and roll into balls. Place the dough balls onto the prepared baking sheets, spacing them about 2 inches apart.
Use a fork to gently press down on each dough ball, creating a crisscross pattern on top.
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 let them cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.