In large bowl, beat margarine and brown sugar until light and fluffy. Add vanilla and egg; blend well. Lightly spoon flour into measuring cup; level off. Stir in flour and baking soda; mix well. Cover with plastic wrap; refrigerate 1 to 2 hours for easier handling.
Heat oven to 375°F. On floured surface, roll out dough, 1/3 at a time, to 1/8-inch thickness, refrigerate remaining dough until needed. Cut out cookies with 1 3/4 to 2-inch cookie cutter. Place 1 inch apart on ungreased cookie sheets.
Bake at 375°F. for 5 to 8 minutes or until light golden brown. Immediately remove from cookie sheets. Cool completely.