Blend together butter and sugar; stir in egg and vanilla. Add flour; mix until well blended. Shape into ball; cover and chill 4 hours to overnight. Roll out dough 1/4-inch thick on a lightly floured surface; cut out with cat-shaped cookie cutters.
Arrange cookies on lightly greased baking sheets; bake at 350° for 8 to 10 minutes, or until golden. Frost cookies with Chocolate Frosting when cool; if desired, sprinkle with black sanding sugar and add candy "eyes." Makes about 2 dozen.
Combine all ingredients in a medium bowl. Beat with an electric mixer on low speed until smooth.