In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until it becomes translucent.
Add the minced garlic and continue sautéing for another minute until fragrant.
Stir in the sour Trahana and cook for a few minutes, allowing it to lightly toast.
Pour in the water or vegetable broth and bring the mixture to a boil.
Reduce the heat to a simmer, cover the pot, and let it cook for about 15-20 minutes or until the Trahana is tender, stirring occasionally.
Season the soup with salt, pepper, and dried mint. Adjust the seasoning to your taste.
Serve hot, garnished with crumbled feta cheese and fresh mint leaves if desired.