In a mixer, beat together butter, oil, sugar, vanilla, and egg.
Add cornstarch, cocoa, and 1 1/2 cups flour. Mix together until dough scrapes itself from the sides. Add flour in 1/4 cup increments to get desired consistency.
Roll dough out to 1/4 inch thickness.
Cut and lay dough on a lined or greased baking sheet.
Bake at 350° for 8-10 minutes.
Allow to cool through, then decorate.