Bring a very large pot of water to a rolling boil to create your court-bouillon base.
Peel and slice the carrot and onion, then add them to the pot along with the bouquet garni for depth of flavor.
Immerse one lobster in the boiling court-bouillon for 10 minutes, then remove and let it cool. Repeat for the remaining lobsters.
Shell the claws and tails from each lobster, cut the tails into medallions, pat dry, and reserve the pieces.
Split the vanilla pod lengthwise, scrape out the seeds with a knife, and set them aside.
In a sauté pan, melt the butter over low heat. Gently warm the chestnuts with the port wine.
Five minutes before serving, add the lobster pieces and vanilla seeds. Stir thoroughly to infuse all elements with the rich flavors.
Season with freshly milled pepper and serve immediately for the best texture and taste.
Happy Holidays, everyone!