Place water, onion, garlic, cinnamon, turmeric, garam masala, salt, and pepper in a large pot; bring to the boil. Add lamb; reduce heat to low and simmer for 15 to 20 minutes. Separate lamb from liquid and set aside. Transfer the liquid to a bowl.

Heat cooking oil in a large, deep skillet over medium heat. Add eggplant slices in a single layer and cook in the hot oil until brown on both sides; remove to a plate lined with paper towels to drain. Use the same procedure to fry zucchini slices, cauliflower, and broccoli.

Layer lamb in the bottom of the large pot. Arrange eggplant, zucchini, broccoli, and cauliflower on top of the lamb in layers. Pour rice over meat and vegetables, shaking the pot gently to allow rice to settle into the dish. Pour reserved cooking liquid from lamb over the mixture until it is completely covered. Add water if needed.

Cover the pot and simmer over low heat until rice is tender and liquid is absorbed, 30 to 45 minutes. Remove the lid from the pot. Place a large platter over the pot and flip the pot so the dish is “upside down” on the platter. Serve with yogurt on the side.