Preheat Oven and Prepare Lamb: Preheat your oven to 350°F (175°C). In a large pot, heat some olive oil and brown the lamb pieces. Season with salt and pepper, and cook until the lamb is tender. This may take about 1 hour. Remove the lamb and set aside.

Cook Rice: In the same pot, cook the rice in boiling water until it's halfway cooked, about 10 minutes. Drain and set aside.

Make Yogurt Sauce: In a separate bowl, whisk together the yogurt and eggs until smooth. Melt butter in a saucepan, add flour, and cook for a couple of minutes. Gradually add the yogurt and egg mixture, garlic, oregano, salt, and pepper. Stir continuously over low heat until the sauce thickens slightly.

Assemble the Dish: In a baking dish, spread the half-cooked rice and place the cooked lamb on top. Pour the yogurt sauce over the lamb and rice, ensuring it's evenly distributed.

Bake: Bake in the preheated oven for 45 minutes, or until the top of the casserole turns a golden brown.

Serve: Let the Tave Kosi cool slightly before serving. It can be enjoyed with a side of fresh salad or your favorite vegetables.