Bring a large pot of water to the boil and boil the lobster for 10 minutes. Remove and leave until cool enough to handle. Preheat the grill to the highest setting.
Once the lobster is cool enough to handle, remove the claws and place on a board. Bash with a rolling pin to break the shell and remove the meat. Place the meat in a bowl.
Lay the lobster body on a board, back side up, and cut it in half along its length using a sharp knife. Make the first cut through the middle of the head. Lay out the halves and remove the meat from the body and tail. Discard the bits from the head.
Clean out the shells, then cut the meat into chunks and place them back into the cleaned shells. Place the halves on a heavy-based small baking tray.
To make the white wine sauce, melt the butter in a small frying pan over a low heat and add the shallots. Cover and cook for 7 minutes until soft. Add the stock, white wine and single cream and bring to a boil. Simmer until it has reached a light sauce consistency. Add the Dijon, parsley and half the parmesan. Season with pepper.
Spoon the sauce over the lobster halves, then top each half with the remaining parmesan. Grill for 2-3 minutes, until the parmesan has melted and coloured lightly. Serve with lemon wedges.