Peel, degerm and crush the garlic.
Peel and cut onion, shallots and carrot into chunks.
Remove the butter out of the fridge.
Rinse the tarragon, remove stems and chop leaves.
Rinse the lobsters with fresh water.
Kill them :
Place the lobster facing you. Enter the tip of a large, sharp knife into the center of the chest (blade towards the head), and slit their heads in length (lower the knife quickly to the front of the animal).
Separate the head from the tail, twisting the tail and pulling.
Detach paws and claws.
Cut (with a bread knife) the tails into 2 or 3 pieces (depending on the size of the lobsters).
Finish cutting the thorax in half, remove the sand sack near the eyes and throw it away (it is not good and sometimes contains pieces of plastic).
Take the "coral" (Roe, the green viscous part) and the liver with a tbsp.
Put them in a bowl.
Put the oil to heat (high heat) in a large frying pan, then sear the lobster pieces with a hint of Cayenne (mix).
Add the garlic, onion, shallots, and carrot.
When the carapace of lobsters is red (it takes 2 to 3 min), stop the hood if any.
Flambé carefully with the brandy (all the water must have dried beforehand so that the alcohol then ignites easily without having been preheated).
Do not do it under a running hood, and pay attention to the flame height!
Add the tomato paste, the crushed pepper and the bouquet garni, mix.
Then deglaze with the white wine and the fish stock. Mix.
Add whatever water is needed to have liquid halfway up the carcasses.
Simmer over medium heat, with a lid.
Once boiling, count 8 min then remove the tail pieces.
2 min after, remove the claws.
Let the sauce simmer at a low heat for another 15-20 minutes.
Meanwhile, peel tails and claws and keep warm.
(you might want to remove the gut from the tails pieces. Make a small cut on the back of the tail to remove it).
Finely chop the roe and the liver.
Mix the butter with 2 tbsp. flour, then add chopped roe and livers.
Remove all the pieces of carcass and bouquet garni from sauce in the frying pan, then blend the sauce.
Add the mixture (roe / liver / flour) to the sauce in small batches, and mix well with a whisk. Cook for 5-10 minutes.
Season to taste (salt/pepper).
The sauce ("Américaine") must be thick and unctuous.
If you have prepared it in advance and need to warm it up, also heat up a bit of Cognac with some crème fraîche in a saucepan and add them to the sauce.
Put lobster pieces on warm plates, drizzle with sauce, and sprinkle with chopped tarragon. (You can also add a few sprigs of chervil).
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