In a medium bowl, mix peanut butter, sugar, egg, and vanilla until well blended.
Place mounds of 1 tablespoon each of cookie batter about 1 inch apart onto ungreased baking sheets. Flatten the mounds with the tines of a fork, making a crosshatch pattern on the cookies.
Bake until golden around edges, about 10 minutes. Transfer to racks to cool. Repeat with the remaining dough.
You can sprinkle these cookies with coarse sea salt, if desired.
