Beat softened butter in a stand mixer until creamy. On low speed, gradually mix in 2 cups of powdered sugar. Add peppermint extract, vanilla extract, and salt; mix until combined. Pour in heavy cream and slowly increase mixer speed to medium. Add the remaining 2 cups of powdered sugar gradually, mixing until the dough is smooth and thick like playdough. Scrape bowl sides often. If the dough is sticky, add more powdered sugar 1 tablespoon at a time. Add food coloring if desired. Roll small portions into ½-inch thick logs. Cut into ¼–½ inch pieces. Place on wax paper and let dry uncovered at room temperature for several hours. Once dry, store in an airtight container with wax paper between layers.