Set up your barbecue for direct cooking. Place the casserole dish (without lid) in the centre and preheat on high for ten 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 one minute, then slowly add the milk and chicken stock. Whisk continuously until thickened. Add the salt, pepper, nutmeg and parmesan and whisk until the cheese has melted. Remove the casserole dish from the barbecue using heat proof/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 oil and preheat for 5 minutes.
Place the onion and garlic in the casserole dish and cook for 3 minutes, or until the onion is tender, opening the lid to stir once. When the onion is cooked add the mince, Italian herbs, cinnamon, salt and pepper to the casserole. Using a spatula, break the mince into smaller pieces. Cook for 12-15 minutes or until cooked through, stirring occasionally. Once the mince is cooked, add the wine and cook for another minute. Remove the casserole dish from the barbecue.
In a large bowl mix the eggplant with the remaining 3 tablespoons of oil, salt and pepper. Once coated, cook the eggplant directly on the grill for 3 minutes a side. When cooked, remove the eggplant from the grill and set aside until needed.
Turn your barbecue to the roast setting (add a convection tray and trivet is 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. Simmer for 30-45 minutes, or until the sauce has thickened. Ensure you keep your barbecue lid down during cooking.
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 approx. one and a half 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 two 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 breadcrumb mixture.
Return the casserole dish without lid to the barbecue. Close lid and cook for 45 minutes, or until the top is golden and bubbling.