Traditionally, homemade matzoon is used, but high-quality, thick plain yogurt with high-fat content (like Greek yogurt) is an excellent substitute. The wheat, known as korkot or dzedzadz (whole, hulled wheat kernels), must be cooked until tender.
A mixture of egg and flour is used to thicken and stabilize the soup, preventing the yogurt from curdling when heated. This soup is most often served cold in the summer, but is also eaten hot in the winter.
Thoroughly rinse the wheat (korkot) and soak for several hours (ideally overnight) if it is not already hulled and quick-cooking.
Cook the wheat in 3 cups of lightly salted water. Boil until tender, about 20-30 minutes. Drain the excess water and set aside.
In a large pot or bowl, combine the matzoon (yogurt), whole egg, and flour. Whisk them thoroughly or use a hand mixer to achieve a completely smooth mixture without lumps.
Gradually pour in the cold water (or broth), continuing to whisk until the mixture is thinned.
Place the pot with the yogurt mixture over medium heat. It is ABSOLUTELY CRUCIAL TO STIR CONTINUOUSLY (ideally with a wooden spoon or whisk) the bottom of the pot. Stir until the mixture begins to bubble and comes to a gentle boil. This stirring prevents the yogurt from curdling into lumps.
When the soup bubbles, add the cooked wheat. Stir and reduce the heat to the lowest setting. Simmer for 5-10 minutes to allow the flavors to meld.
Melt the butter in a small skillet. If using onion, sauté it in the butter until translucent.
Add the dried mint (or fresh) and cook for 30 seconds until the aroma is released (be careful not to burn it).
Salt the soup to taste (add salt only at the end; if added earlier, the yogurt may curdle).
Serve hot: divide the soup into bowls and drizzle each portion with the hot mint butter.
If you want to serve the soup cold, let it cool completely at room temperature, then place it in the refrigerator. The butter is also served on cold soup, but chilled.