Preheat oven to 350 degrees. Line a baking sheet with parchment paper; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat together peanut butter, egg, sugar, baking soda, vanilla, if using, and salt until well combined.
Using a 1 3/4-inch scoop, scoop dough onto prepared baking sheet, spacing 2 inches apart. Using the tines of a fork, gently press down on each scoop in a crosshatch pattern. Sprinkle with sugar and transfer baking sheet to oven. Bake until slightly puffed, 11 to 12 minutes. Cookies will still be soft. Let cool for 5 minutes. Carefully transfer cookies to a wire rack and let cool completely.