Preheat oven to 350°F (175°C). Beat peanut butter, brown sugar, granulated sugar, egg, and vanilla until smooth and glossy.

Stir in baking soda and salt until no dry streaks remain. The dough will stiffen.

Scoop rounded tablespoonfuls of dough, roll into balls, and place 2 inches apart on lined baking sheets. Press each ball with a fork in a crosshatch pattern to flatten.

Bake 10 to 12 minutes, until edges are set and lightly golden but centers look soft. Cool on the sheet 5 minutes, then transfer to a rack. Stack once fully cooled.