Lamb Baked in Yogurt

Name: Lamb Baked in Yogurt
Ingredients: 2 Tablespoons extra-virgin Greek olive oil; 1 Tablespoon unsalted butter; 1 Pound boneless leg of lamb or goat, cut into 2-inch chunks; 4 scallions, trimmed and chopped finely; 2 cloves garlic, minced; 1/2 Cup basmati or another long-grain rice; 1/2 Cup dry white wine; 1 Cup water; Salt and pepper, to taste; 2 large eggs; 2 Cups thick Greek yogurt; 3 Tablespoons all-purpose flour; 2 Tablespoons finely chopped fresh mint; 3 Tablespoons grated kefalotyri cheese (optional)