In a large bowl, use an electric mixer to combine the butter, shortening, and sugar. Blend in the flavoring and flour. Shape into balls and set on a cookie sheet 2-inches apart.
Bake at 350 degrees for 8-10 minutes. If using cherries, press 1/2 of a maraschino cherry in the center of each cookie as soon as they come out of the oven. Let cool for several minutes before transferring them to a wire rack to cool completely.
Here are a few more butter cookie recipes you might enjoy: