Preheat oven to 350°F and line two baking sheets with parchment paper.
Mix together peanut butter, sugar, egg, vanilla extract, baking soda, and salt in a large bowl until smooth and well combined.
Roll dough into 1-inch balls and place them 2 inches apart on the prepared baking sheets.
Use a fork to press a crisscross pattern into each cookie, flattening them to about 1/4-inch thickness, then sprinkle lightly with additional sugar.
Bake for 8-10 minutes until edges are just golden but centers still look slightly soft.
Let cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.