Set up your barbecue for direct cooking. Please refer to your handbook for further instructions. Place a large Weber Ware Frying Pan directly on the grill and preheat your barbecue for barbecuing. Once the barbecue has preheated, adjust the burner control(s) to medium-high heat.
Add 2 tablespoons olive oil to the frying pan, and then add the shallots, garlic, and speck, stirring every couple of minutes. Cook, with the lid closed, until the onion is browned, about 4 minutes.
Lightly oil the lamb steaks and season with salt and pepper. Place the steaks directly on the grill and cook for 2 minutes on each side. Remove from the grill.
Add the plain flour to the frying pan and cook for 2 minutes, with the lid closed, stirring every minute. Add the red wine, beef stock, tomato paste, and bay leaves. Bring to a gentle simmer, then remove the pan from the barbecue.
Set the barbecue up for indirect cooking (please refer to your handbook for further instructions). Roughly cut the lamb steaks into 2cm cubes. Return the frying pan back to the barbecue and add the lamb cubes to the sauce. Place a layer of alfoil on top of the frying pan and cook until the lamb is tender, about 1½ hours on the roasting setting.
While the lamb is cooking, make the polenta mash. In a large saucepan over high heat on a side burner or stove top, bring the water to a boil. Add the polenta, stirring every couple of minutes. Once the polenta has thickened and has come to a boil, turn the burner to low. Continue to cook for 15 to 20 minutes, stirring every couple of minutes. Once cooked, turn the burner off and stir in the cream, ⅓ cup of the Parmesan cheese, the butter, salt, and white pepper.
Remove the alfoil from the frying pan and spoon the polenta on top of the lamb filling. Top with the remaining ⅓ cup Parmesan cheese and the thyme. Return the pie back to the barbecue and cook until the Parmesan cheese is golden, a further 25 to 30 minutes on the roasting setting.