First, preheat the oven to 375 degrees.
Heat a large saucepan over medium-high heat and add the olive oil and 3 tbsp. butter.
Toss the lamb with 1⁄4 cup flour and season with salt and pepper.
Add the lamb to the saucepan and cook for 10–12 minutes and don't forget to turn it from time to time until it starts getting brown.
Then add to the saucepan garlic, rice, and 1⁄2 cup water and let it boil.
After it starts boiling reduce heat to medium-low and cover it. Cook for another 15-20 minutes until rice is softened or tender.
Add to the pan salt, pepper and oregano, stir well and transfer it to a baking dish.
You can use the same saucepan and add the rest of the butter and turn the heat to medium-high.
Add remaining flour and whisk until you get smooth and cook it for about 2 minutes.
Now you can turn off the heat and take it off. Add nutmeg, yogurt, eggs, salt, and pepper and whisk until smooth.
Cover the lamb mixture in the baking dish with this yogurt sauce.
Place it in the oven and bake for about 45–60 minutes or until the lamb gets tender.