Preheat oven to 350 degrees and grease baking sheets. In a bowl with an electric mixer beat together peanut butter and sugar until combined well. In a small bowl lightly beat egg and beat into peanut butter mixture with baking soda until combined well.
Roll level teaspoons of dough into balls and arrange about 1-inch apart on baking sheets. With tines of a fork flatten balls to about 1 1/2 inches in diameter, making a crosshatch pattern. Bake cookies in batches in middle of oven until puffed and pale golden, about 10 minutes.
Cool cookies on baking sheets for 2 minutes and transfer with a metal spatula to racks to cool completely. Cookies may be kept in an airtight container at room temperature up to 5 days.