Preheat oven to 350°F. Line two baking sheets with parchment paper.
Cream peanut butter with both sugars in a bowl until smooth and slightly fluffy.
Beat in the egg and vanilla until fully incorporated.
Sprinkle in baking soda and salt. Mix just until the dough comes together.
Scoop 1-tablespoon portions, roll into balls, and space 2 inches apart on the sheets.
Press each ball with a fork in a crisscross pattern to flatten slightly.
Bake 9–11 minutes, until edges are set and tops look dry. Do not overbake.
Cool on the pan for 5 minutes, then transfer to a rack to finish cooling.