Let the Greek yogurt stand at room temperature while you prepare the cooler and the milk mixture.
Fill three 1-quart plastic containers or glass jars with hot tap water (about 115 degrees F); cover. Place the containers in a small insulated cooler and pour in enough hot water (115 degrees F) to come about 2 inches up the sides. Close the cooler and let it preheat. Rinse two more 1-quart containers or glass jars with hot water (115 degrees F); set aside.
Add a splash of water to a large saucepan and swirl to coat the bottom of the pan (this will help keep the milk mixture from scorching). Add the half-and-half and milk to the saucepan and bring to a simmer (180 degrees F to 190 degrees F) over medium-low heat, stirring frequently with a rubber spatula to prevent a skin from forming and to prevent the mixture from scorching.
Remove from the heat and allow the temperature to drop to 115 degrees F. Whisk in the Greek yogurt until smooth, then pour the mixture into the empty containers and cover. Place the containers in the cooler and pour in enough hot water (115 degrees F) to reach just below the lids of the yogurt containers. Close the cooler and let sit, undisturbed, 5 hours. (Or, for tangier yogurt, let the yogurt sit up to 24 more hours, changing out the water a few times to maintain 115 degrees F.)
Remove the yogurt from the cooler and refrigerate until cold, about 2 hours.
For thicker, Greek-style yogurt, line a fine-mesh sieve with 4 layers of cheesecloth and set over a large bowl. Pour in the yogurt, cover with more cheesecloth and let drain in the refrigerator until it's as thick as you like, or up to 2 hours.
Mix in honey and toasted sliced almonds.
Mix in chopped mandarin oranges and toasted coconut flakes.