Add the butter to your stand mixer and beat it smooth.
Add the sugar, half and half, vanilla, and peppermint extracts and beat on low until it's crumbly.
Add in your food coloring. I divided the batch into thirds and uses three drops of color for each, beating them until it was well-mixed, then removing it and repeating with the other colors.
Sprinkle a flat surface with powdered sugar like you're dusting with flour, and roll out your mint dough into a long, thin log. Pretend you're a kid making snakes out of play-doh.
Cut the mints into the size and shape you want, and arrange them on your tray to dry out. Leave these exposed to dry for at least 24 hours, or as long as you want to get the texture you prefer. The exact time will vary depending on your location, weather, and time of year!