1. Cook and shell the lobsters. 
2. Cut the lobster tails into medallions. 
3. Peel the little potatoes, cut them into halves or quarters and give an initial cooking in oil.
4. Turn the artichokes, leaving on the stems; quarter them and cook in olive oil, lemon juice and white stock. 
5. Reserve 4 raw pieces, slice them thinly and fry them.
6. Sauté the potatoes and artichokes in olive oil until lightly colored; add the lobster and butter and finish with chopped tarragon. 

Anchoiade Sauce and Presentation

1. Place into a blender in order: egg yolk, garlic, anchovy, white stock, oils and lemon juice. Season. 
2. In the center of the plate, place the sautéed lobster, potato and artichoke with a ribbon of sauce around, the dressed arugula and olive oil on top, and then the artichoke chips. 
3. For garnish: 2 chive spears, half a lobster head cut on a bias and olive oil.