1. In a large enameled cast-iron casserole, heat 2 tablespoons of the olive oil until shimmering. Working in batches if necessary, add the lamb and season with salt and pepper. Cook over moderately high heat until browned all over, about 6 minutes. Transfer the lamb to a shallow bowl.
2. Add the garlic, onion and the remaining 1 tablespoon of olive oil to the casserole and cook over moderate heat until softened. Add the carrots and spices and cook, stirring, until fragrant, about 2 minutes. Stir in the flour and add the lamb and water. Bring to a boil, stirring to scrape up any browned bits from the bottom of the casserole. Reduce the heat to low and simmer uncovered, stirring occasionally, until the lamb is tender and the sauce is thickened, about 1 1/2 hours. Raise the heat to moderately high and stir in the spinach until wilted. Season with salt and pepper. Spoon the lamb stew into 4 shallow 2 1/2-cup glass or ceramic baking dishes.
3. Meanwhile, preheat the oven to 425°. In a medium saucepan, mash and stir the sweet potatoes over high heat until warmed through. Mash in the goat cheese, milk and butter and season with salt and pepper.
4. Spread the mashed sweet potatoes over the lamb stew and bake for about 10 minutes, or until hot and bubbling at the edges. Preheat the broiler. Broil the topping 4 inches from the heat until golden, about 1 minute. Serve at once.