Boiled Lobster with Lobster Essence Mayonnaise

Bring water, sea salt, and white vinegar to a rolling boil in a large stockpot. Humanely dispatch the live lobsters immediately before cooking by piercing the back of the head swiftly with a heavy chef's knife.

Plunge the dispatched lobsters headfirst into the boiling water. Boil for exactly 7 minutes for 600g lobsters. The shell should turn bright red, and an instant-read thermometer inserted into the thickest part of the tail should register an internal temperature of 60 degrees Celsius or 140 degrees Fahrenheit.

Using tongs, immediately transfer the lobsters to an ice bath setup to halt the cooking process. Allow them to cool for 5 minutes.

Remove the lobsters from the ice bath. Separate the tails, claws, and knuckles from the carapace. Carefully extract the meat using kitchen shears, keeping it as intact as possible. Reserve the meat in the refrigerator. Save all the shells and heads.

Using the kitchen shears or chef's knife, chop the reserved lobster shells into small, 2-centimeter pieces. Discard the feathery gills and the sand sac located near the head.

Heat a heavy saucepan over medium-high heat. Add the chopped shells and dry roast them until deeply red, fragrant, and slightly charred at the edges, about 5 minutes.

Stir the tomato paste into the shells and cook for 1 minute to caramelize. Deglaze the pan with cognac, scraping up any browned bits from the bottom.

Pour the grapeseed oil over the shells. Bring the oil to a gentle simmer at 85 degrees Celsius or 185 degrees Fahrenheit. Maintain this temperature for 15 minutes, then remove from heat. Allow the mixture to steep for 45 minutes.

Strain the infused oil through a fine mesh sieve lined with cheesecloth into a clean container. Discard the shells. Allow the vibrant red lobster oil to cool completely to room temperature.

In a clean mixing bowl, combine the room-temperature egg yolks, dijon mustard, lemon juice, sea salt, and white pepper. Whisk vigorously until the mixture is smooth and slightly pale.

While whisking continuously, slowly add the cooled lobster oil drop by drop to form a stable emulsion. Once an emulsion forms, gradually increase the flow to a thin, steady stream until all the oil is incorporated and the mayonnaise is thick and glossy.

Slice the chilled lobster tails into elegant medallions. Arrange the meat artfully on cold plates alongside whole claw meat. Serve the lobster mayonnaise in a small ramekin alongside the dish, or pipe neat dots around the plate for a modern presentation.