How to Make It
Fill a large stockpot with 2 inches of water, add the salt and bring to a boil over high heat. Put the lobsters in the boiling water, head first, and cook until they start to turn red, about 4 minutes. With tongs transfer the lobsters to a bowl to cool.
Remove the meat from the lobster knuckles and claws. Twist the tails off the bodies; reserve the greenish tomalley and blackish roe (the roe doesn't turn red until it's fully cooked). Split the tails lengthwise and remove the tail meat. Pull out and discard the black intestinal vein. Cut the tail meat into 1-inch chunks. Cover and refrigerate the lobster, tomalley and roe.
Crush all the lobster shells and place in a large saucepan. Add 6 cups of water and simmer over moderate heat for 20 minutes. Strain the broth through a fine sieve, pressing hard on the shells to extract as much flavor as possible. Return the broth to the saucepan. Add the milk and cream and simmer over low heat for 5 minutes.
In a large skillet, melt the butter over moderate heat. Add the crushed crackers and stir until lightly toasted, about 2 minutes. Stir the crackers and the lobster meat into the soup and simmer very gentlythe stew must never come near a boilover low heat for 1 hour, stirring occasionally. Gently whisk in the reserved tomalley and roe. Season with salt and pepper and a pinch of cayenne. Serve the stew with the additional oyster crackers.