Kill the lobster by plunging a sharp knife into the cross at the head.
The brain is behind this.
Now split right down the center into two halves.
Remove the sac that is near the head, and the thread of gut.
Crack the claws to allow the heat to penetrate.
Paint the shell and claws with melted butter, and spread soft butter over the upturned flesh of the demi lobsters.
Put under the broiler until it begins to color.
Add more butter if necessary, and transfer to a moderate oven (350°) for 5 to 7 minutes more to finish cooking. (You can't turn the half lobster on the broiler or all the juice will run out.)
Cover with greased aluminum foil or wax paper while in the oven to prevent the flesh from drying out.
Sprinkle with coarse salt and serve.
If you have started off with a lobster that is fresh from the lobster pots, you will have that delicious cream in the body of the lobster.