Whisk together the flour, baking soda, and salt in a medium bowl. In a separate large bowl, beat the softened butter, peanut butter, granulated sugar, and brown sugar for 2–3 minutes, until smooth and creamy.

Beat the egg and vanilla into the peanut butter mixture until fully incorporated. Add the dry ingredients and mix just until no streaks of flour remain; do not overmix.

Portion the dough into roughly 1 1/2-tablespoon balls. Roll them in the optional granulated sugar, then chill the shaped dough for at least 1 hour.

Heat the oven to 350°F (175°C) and line baking sheets with parchment. Arrange the chilled dough balls about 2 inches apart and press each one lightly with a fork in a crisscross pattern.

Bake each batch for 11–12 minutes, until the edges look set but the centers still appear slightly soft. Cool the cookies on the baking sheet for about 5 minutes before transferring them to a rack.