Set up your barbecue for direct cooking. Place the Weber Ware Casserole Dish (without lid) in the centre and preheat on high for 10 minutes.
Once your barbecue is preheated, leave the heat setting on high. To make the béchamel sauce, add the butter to the casserole dish, stirring until just melted. Add the flour and whisk until smooth. Cook for 1 minute, then slowly add the milk and chicken stock. Whisk continuously until thickened. Add the nutmeg and Parmesan and whisk until the cheese is melted. Season with salt and white pepper. Remove the casserole dish from the barbecue wearing heatproof/oven gloves. Pour the béchamel sauce into a jug and wash out the casserole dish.
Place the casserole dish directly on the barbecue grill. Add 2 tablespoons of the oil and preheat for 5 minutes.
Place the onion and garlic in the casserole dish and cook until the onion is tender, about 3 minutes, stirring once. Add the lamb mince, Italian herbs, and cinnamon, and season with salt and pepper. Using a spatula, break the mince into smaller pieces. Cook for 12 to15 minutes or until cooked through, stirring occasionally. Add the wine and cook for another minute. Remove the casserole dish from the barbecue.
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In a large bowl mix the eggplant with the remaining 3 tablespoons of oil, and season with salt and pepper. Grill the eggplant for 3 minutes a side. Remove from the grill and set aside until needed.
Turn your barbecue to the roast setting (add a convection tray and trivet if using a Q). Add the passata sauce and lemon zest to the casserole and stir through. Place the casserole dish (without lid) on the trivet, and close the grill lid. Simmer until the sauce has thickened, 30 to 45 minutes.
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In a bowl mix the topping ingredients together and set aside until needed.
Remove the casserole dish from the barbecue and pour the mince mixture into a bowl. Spoon about 1½ cups of the mince mixture back into the casserole dish and spread evenly over the base. Place a layer of the grilled eggplant over the mince. Then spoon 2 cups of the remaining mince mixture on top of the eggplant. Repeat this process one more time and then pour the béchamel sauce on top. Finish the moussaka by sprinkling the top with the bread crumb mixture.
Return the casserole dish (without lid) to the barbecue. Close the grill lid and cook until the top is golden and bubbling, about 45 minutes.