Preheat oven to 375 degrees F. Grease cookie sheets and set aside. In a medium bowl, stir together the 1 cup sugar, the peanut butter, and egg until well mixed. Using your hands, roll peanut butter mixture into 1-inch balls; place 2 inches apart on prepared cookie sheets. Flatten each ball slightly with a drinking glass that has been lightly greased and dipped in sugar. Lightly grease a small star-shaped cookie cutter; dip in sugar. Press into the center of each cookie.

Bake about 9 minutes or until edges are set and bottoms are lightly browned. Makes 36 cookies.