For the Shrimps:
Sear the shrimps with the prepared shellfish butter and season with sea salt and pepper to taste.

For the Lobster:
Reduce the white wine over heat in a saucepan to half its original volume and then pour in orange juice and bring the liquid to a boil. Season with salt and pepper and a drop of lemon juice. Then poach the lobster half in the butter mixture until the lobster is medium rare. Discard the tail.

For the Whipped Cream Dressing:
Beat the whipped cream with grated lemon peel, lemon juice and pepper until well blended.

For the Lobster Soup:
Reduce the reserved lobster broth in a pot over heat, until the flavors are as intense as desired, then add in the fresh butter and a drop of lemon juice. Thicken the sauce with corn starch, and pour it into a coffee pot to serve.

For the Chestnut Puree:
Pour the chicken stock in a soup pot, add the chestnuts and butter and then bring stock to a boil. Reduce heat and slowly simmer for 30 minutes until the chestnuts are tender, then strain away the stock and pass the chestnuts through a Japanese sieve.

For the Lobster Broth:
Saute the lobster head pieces for a few minutes in a pan, then pour in some olive oil and saute the lobsters until the shells start to turn color. Then add the garlic, fennel and shallots and simmer slowly. Next add the diced tomato and continue sauteeing until the sauce thickens. Then add the tomato paste, 185ml Martell Cognac and white wine. Reduce the liquid to half its original volume, then pour in the chicken stock and slowly simmer for 1 hour, skimming the surface occasionally to clear the broth. Finally, season with chili pepper and strain the broth through a fine sieve. Reserve 60ml of the broth for the whipped cream sauce.

Bring the rest of the lobster broth to a boil in a clean pot, then stir in prepared chestnuts puree, 30ml Martell Cognac and slowly simmer for 20 minutes. Melt butter into the broth, then transfer to a blender and blend until smooth. Season with sea salt and pepper to taste; strain through a muslin cloth. Just before serving add a drop of lemon juice to emulsify the broth.

For the Shellfish Butter:
Heat some olive oil in a saucepan and add the chopped lobster shells. Saute slowly until they turn color, then add the shellfish broth and water and continue to simmer for 10 minutes. Finally, add clarified butter and allow the mixture to slowly simmer for another 1 hour until the liquid has been reduced to half its original volume and the butter becomes clear. Strain and then refrigerate in ice water bath.