Beat butter, cream, salt, peppermint oil, and ¾ cup of powdered sugar in a Kitchenaid till very smooth and creamy.
Slowly add in the remaining powdered sugar, scraping the sides of the bowl often.
You can make all one color, or divide the dough into 4 portions. For each portion add a different food color and beat for 2-4 minutes, or till smooth and fluffy.
Scrape each color mixture into a mound, and wrap tightly with plastic wrap. Chill for at least an hour.
When the mixture is firm enough to handle, divide it into 5 or 6 pieces. To form mints, sprinkle your counter liberally with powdered sugar. Roll each piece out into a rope about ½" thick.
Alternatively, shape the pieces to create mini mint balls or roll the candy out like cookie dough and use mini cutters to stamp out different shapes.
Use a dough scraper to cut each rope into small pillow-shaped pieces approximately ½" long. Place each mint on a cookie sheet lined with waxed paper. Let mints sit at room temperature for at least 12 hours to dry out.