Preheat oven to 350º. Coat baking sheets with non-stick cooking spray.
With an electric mixer, beat peanut butter and sugar until combined. Beat in egg and vanilla. Sprinkle baking soda over mixture; beat until combined.
Measure heaping teaspoon size pieces of dough. Roll between your palm to make balls; arrange about 1-inch apart on baking sheet. With the tines of a fork, flatten balls to about 1-1/2 inch in diameter, making a crisscross pattern.
Bake cookies in batches until puffed and pale golden, about 8-10 minutes (don't overbake).
Let cool on baking sheet 2 minutes. (This is important because they are fragile when hot from the oven, and they need time to 'set up'). Transfer with a spatula to racks to cool completely.
Makes about 40-60 cookiesRecipe submitted by ~Donna~ V on 9/27/00