Step 1

If using live lobsters, prepare to steam them. Note: There are lots of opinions on the most humane way to cook a lobster—choose the method you're most comfortable with. If you'd like to quickly kill the lobsters before cooking, Fine Cooking has a very clear video: https://www.finecooking... Alternatively, you can numb them in the freezer for 20 to 30 minutes (though you may need to add an extra minute of cook time) or stand the lobsters on their heads to calm them, like this: https://food52.com/blog...

Step 2

To steam the lobsters, fill a large, tall, lidded pot with 1 inch of salt water. If the lobsters do not fit comfortably in the pot and you cannot see the bottom of the pot, it’s overcrowded and you should use more than one pot. Set up a steaming rack inside the pot (or improvise one with an upside-down colander)—there should be enough room that the lobsters will be suspended far enough above the water that when they release liquid during steaming, they do not end up sitting in it. Turn the heat to high and cover the pot. The water will boil quickly and fill the pot with steam. When it does, place the lobsters in the pot and cover tightly. 1-pound lobsters should take 10 minutes to cook; add 2 minutes for every additional 1/4 pound. Halfway through steaming, using long tongs, carefully rearrange the lobsters. Work quickly and cover the pot again as soon as possible. When the lobsters have cooked for the recommended time, remove one and break it open where the carapace meets the tail. The tail meat should be creamy white with no translucency. If not, allow the lobsters to steam for a few minutes more.

Step 3

Let the lobsters cool at room temperature. Use a cleaver to crack and remove the meat from the claws, knuckles, and tails. Remove the cartilage from the claws and the intestine from the tails of the cooked meat and discard. Cut the meat into 1/2-inch dice. You may pick all the meat from the carcass or freeze the carcass for soup or broth.

Step 4

Place the cucumber in a colander for at least 5 minutes to drain any excess liquid.

Step 5

Combine the lobster, cucumber, and mayonnaise. If the salad is to be served within the hour, add the scallions. If not, add them 30 minutes before serving. Season with salt if needed and pepper. Cover with plastic wrap and chill for at least 30 minutes before serving.

Step 6

When ready to serve, preheat a large heavy skillet (12 or 14 inches) over medium low heat. (A black cast-iron pan is perfect.)

Step 7

Lightly butter both sides of each bun. Place in the pan and cook for about 2 minutes or until golden brown. Turn the buns over and toast the other side. Or toast them under the broiler instead.

Step 8

When the buns are ready, stuff them with the chilled lobster salad. Place each roll on a small paper or china plate; garnish with pickles and potato chips. Serve at once, while the bun is still warm and salad cold.

Step 9

To make the mayonnaise by hand (alternatively, these steps can be done in a food processor): Place a stainless-steel mixing bowl on a damp cloth to keep the bowl from sliding around. Add the egg yolk, mustard, and tarragon to the bowl and whisk until blended.

Step 10

Drizzle the oil into the bowl while whisking constantly. Be sure that the mixture is smooth and well blended at all times. Stop adding the oil periodically to allow yourself time to catch up; when there is no oil visible, continue adding and whisking. When half the oil is added, add 1 teaspoon of lemon juice. Alternate between the remaining oil and lemon juice, whisking all the while, until both are incorporated.

Step 11

Whisk in the ice water. (The water stabilizes the mayonnaise, which prevents separating, a common flaw of homemade mayonnaise.) Season to taste with salt pepper and cayenne. Whisk. Store in a small container, covered and refrigerated, for up to 3 days. Makes 1 cup.