Cream butter in a medium mixing bowl; gradually add sugar, beating until light and fluffy. Add egg; beat well. Add flour alternately with milk, beginning and ending with flour. Mix well after each addition. Stir in vanilla.
Brush pizelle or waffle iron with oil; preheat iron 2 minutes. Place 1 heaping teaspoon of batter in center of iron; close iron, and bake 1 minute or until lightly browned. Remove wafer, and quickly roll up; cool on a wire rack. Repeat procedure with remaining batter. Store wafers in an airtight container.
Note: These wafers are delicious served with ice cream.