Beat butter at medium speed of an electric mixer until creamy. Gradually add brown sugar, beating well. Add egg and vanilla, beating well.
Combine flour, soda, and salt; add to butter mixture, beating just until blended.
Roll dough to 1/4" thickness between two sheets of wax paper. Cut with 4" cookie cutters. Place 1" apart on ungreased cookie sheets. Sprinkle cookies with decorator sugar.
Bake at 350° for 10 to 12 minutes. Let cookies cool 1 minute on cookie sheets, and carefully transfer to wire racks to cool completely.