Cream the butter, oil, sugar, vanilla and salt in the bowl of a stand mixer fitted with a paddle attachment, just until the mixture is smooth. (Do not over beat, as this will incorporate air into the dough, which may lead to spreading.)

Add the egg and mix just until incorporated.

Mix in the cornstarch, cocoa powder and 1 1/4 cups of the flour.

Continue adding flour until the dough gathers itself into a ball and pulls away cleanly from the sides of the bowl.  (You may not need all the flour.)

Preheat the oven to 375 degrees F.

Roll the dough to a thickness of 3/8-inch, between two sheets of parchment paper. (Rolling pin rings will help you to achieve an even thickness.)

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, then decorate with royal icing.