Cut the lobster in half lengthwise, and remove the meat from the claws and tail. Leave to one side. Remove any meat from the head and set aside. Cut the meat up into pieces and place back into the shell.
Melt the butter in a large skillet over medium heat. Add the shallot; cook and stir until tender. Mix in the fish stock, white wine and double cream. Bring to a boil, and cook until reduced by half. Mix in the mustard, lemon juice, parsley, salt and pepper.
Preheat your oven's broiler.
1 medium (1 1/2 pound) cooked lobster
2 tablespoons butter
1 shallot, finely chopped
1 3/8 cups fresh fish stock
1/4 cup white wine
1/4 cup double cream
1/2 teaspoon hot English mustard
1 tablespoon fresh lemon juice
2 tablespoons chopped fresh parsley
salt and freshly ground black pepper to taste
1/4 cup freshly grated Parmesan cheese