Beat butter, cream, salt, peppermint oil, and 3/4 cup of the powdered sugar in a Kitchenaid mixer till very smooth and creamy.
Slowly add in the remaining powdered sugar, scraping the sides of the bowl often. Add food coloring if desired. Beat for 2-4 minutes, or till smooth and fluffy.
Scrape all of the mixture onto a large piece of plastic wrap. Wrap tightly. Chill for at least an hour.
When 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 1/2" thick.
Use a dough scraper to cut each rope into small pillow shaped pieces approximately 1/2" 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.
Notes
I used food grade peppermint essential oil, but you can also use the peppermint oil you find on the candy making isle.