Preheat the oven to 375°
Cream together the butter, oil, sugar, vanilla and salt in a large mixing bowl, just until the mixture is smooth.
Add the egg and mix just until incorporated.
Mix in the cornstarch, cocoa powder and 1 1/4 cups of flour. The dough should form into a ball and pull away from the sides of the bowl. Add more flour by the tablespoonful if necessary.
Roll the dough to a thickness of 3/8-inch, between two sheets of parchment paper.
Cut shapes using a cookie cutter.
Bake on parchment-lined baking sheets for 9 to 12 minutes, or until the cookies look dry on the surface, and feel firm around the edges and set in the middle.
Cool completely before decorating