I recommend using a crusting buttercream when decorating buttercream sugar cookies. This allows the buttercream to form an outside crust, giving them a bit more protection from getting accidentally squished. This is essential if you plan to transport these cookies from your house to another location or if you want to stack or seal them.
In your electric mixer, use the paddle attachment to mix the butter and vegetable shortening together.
Slowly mix in the powdered sugar, only adding as much as your electric mixer can handle at a time.
Mix in the vanilla extract and 2 tbsp. of milk. If the mixture is too stiff, add more milk. I prefer a consistency of smooth peanut butter for cookies that have a lot of line work and a slightly stiffer consistency for piping flowers.
Notes
This recipe will store nicely in the fridge for a few weeks in an airtight container. You can also leave your decorated cookies at room temperature for several days, as the frosting will be shelf-stable due to the mixture of sugar and fat.