Take cheesecloth and tie a sheet of it over a large bowl. Pour yogurt onto this cheesecloth and refrigerate for 2 to 3 hours to let it drain. Press yogurt firmly with a spoon to let out any excess liquid. Any yogurt left should be thick. Transfer to a clean bowl.
Take the saffron threads and soak in warm milk for 10 minutes before stirring into the yogurt. Add your sugar, pistachio nuts, and cardamom here too. Stir food coloring if using, and refrigerate until completely chilled, about 1 hour.