Simmer the lobster for between 12-20 minutes, depending on size. Cut the lobster into halves and remove the meat from claw and tail. Clean the head. Cut the meat into bite-sized pieces and put it back into the lobster shell.
At the barbecue:
Prepare the barbecue for direct heat using the GBS Wok, approx. 180 to 200°C. Melt the butter, add the shallots and sauté lightly. Deglaze with wine. Let it reduce, add the fish stock and the crème fraiche. Now let it reduce by half. Add mustard, lime juice, and parsley and then season with salt and pepper.
Remove the Wok from the heat and prepare the barbecue for high indirect heat (220–250°C). Cover the lobster with the sauce and sprinkle with parmesan. Place the lobster on a grilling basket on an indirect heat. Bake for 15 minutes until the lobsters are golden brown.