In large bowl, mix sugar and butter. Beat in egg and vanilla until light and fluffy. Mix in flour and baking soda.
Divide dough into halves. Shape each half into roll about 1 1/2"-inch in diameter. Wrap each half in wax paper and refrigerate for approximately 1 hour until chilled.
Preheat oven to 375. Unwrap rolls and cut into 1/4"-inch slices. Sprinkle each slice with a pinch of sugar. Place on ungreased pan and bake 10-12 minutes or until lightly browned around the edges. Cool on wire rack. Store in air tight container once the cookies have cooled.