Set up your barbecue for direct cooking. Place a casserole dish (without lid) at the centre of the grill and add the oil. Preheat on high for ten minutes.
Lightly oil the steak and season with salt and pepper.
Once your barbecue is preheated, leave the heat setting on high. Add the onion, garlic, prosciutto and mushrooms to the casserole dish and cook, stirring occasionally, for 5-6 minutes. At the same time, add the beef to the grill around the casserole dish. Cook for 3-4 minutes per side, 6-8 minutes in total. When the onion mixture is cooked, add the flour and stir through, then add the beef from the grill.
Remove the casserole dish from your barbecue using heat proof/oven gloves.
Turn your barbecue to the roast setting (add a convection tray and trivet if using a Q) using tongs and/or heat proof gloves.
Add the stock and wine to the casserole, stir through, then add the thyme and bay leaves. Place the lid on the casserole dish and place on the barbecue. Cook for 2 hours.
In a bowl rub the butter into the self-raising flour. Stir in the parmesan and the milk. Combine well. Roll into approx. 25-30 small balls and place on top of the casserole. Leave the lid off the casserole dish and cook for 20-25 minutes, until the dumplings are golden and cooked through.