Preheat the oven to 350 degrees F and place racks in the upper and lower third of the oven.

In a medium bowl, mix the peanut butter, sugar, egg and vanilla until well combined. Spoon 1 tablespoon of mixture about 1 inch apart onto ungreased baking sheets. Flatten the mounds with the tines of a fork, making a crosshatch pattern on the cookies. Sprinkle coarse salt on top of the cookies.

Bake until golden around edges, about 10 minutes, switching the position of the pans halfway thorough baking. Transfer to racks to cool. Repeat with the remaining dough.

What Makes This Recipe Really Sing: Without the flour getting in the way, you really get that true peanut butter flavor.