Bring a pan of well-salted water up to the boil and carefully drop in the lobster. Bring back to the boil and cook for 6 minutes. The lobster is only partly cooked at this point, as it will be cooked more under the grill. Remove from the water with tongs, put on a board and allow to start cooling.
In the meantime, sauté the shallot gently in the butter for 8 mi