If desired, freeze the lobsters for 2 hours to sedate them before cooking. For a similar treatment with a little more zip, see Singaporean Chilli Crab.
Place on a rimmed baking sheet to catch any juices:
Kill them by cutting through the head as directed. Cut through the body and back through the tail, severing the carapace in half. Cut off the claws and crack them once or twice to expose the meat. Remove and discard the head sacs and tail veins. Reserve the coral, if present, and tomalley for the sauce, if desired. Cut the tail halves from the body. Melt in a large skillet over medium heat:
Add and cook until softened:
Add the lobster pieces still in the shell. Cook, stirring frequently, until the shells are red, about 4 minutes. Add to the skillet:
Flambé. Add to the skillet to extinguish the flames:
Add any reserved lobster juices, the coral, and tomalley, if using. Simmer about 15 minutes. Meanwhile, mash together with a fork until the mixture forms a paste:
Transfer the lobster pieces to a serving dish and whisk the butter-flour mixture into the sauce along with:
Simmer briefly to slightly thicken the sauce. Pour the hot sauce over the lobster and garnish with: