Beat butter and shortening at medium speed with an electric mixer until creamy; gradually add sugars, beating well. Add eggs, 1 at a time, beating until blended after each addition. Stir in vanilla.
Combine flour and next 3 ingredients; add to butter mixture, beating until blended.
Fold in chocolate morsels and crushed peppermint candy; drop dough by rounded tablespoonfuls, 3 inches apart, onto lightly greased baking sheets.
Bake at 350° for 12 to 14 minutes (do not overbake). Transfer to wire racks to cool.