For the Artichoke Puree: Cut the artichoke into medium size pieces and place in a pot. Cover the artichokes with milk and cream. Bring to a boil and reduce to a low simmer. Cook the artichokes until very tender. Strain the artichokes (reserving the liquid). Transfer to a food processor. Add a little of the reserved cream if needed. Add the mascarpone and goat cheese and blend for 10 more seconds or until well mixed together. Season with salt and pepper if needed. Stir in the butter. Transfer to a container and keep warm.
For the Choron sauce: In a small saucepan, combine the shallots, pepper, white wine, and vinegar. Reduce over medium heat until 2 tablespoons of liquid remains. In a heat-resistant mixing bowl, combine the egg yolks, water, salt, and shallot mixture. Whip over hot, but not boiling, water until thick and creamy. Slowly whisk in the melted butter, a few drops at a time, until the sauce begins to emulsify. In a slow stream, whisk in the remaining butter until it is completely incorporated. Whisk in the tarragon. Correct seasoning, to taste. Whisk the chopped tomato or tomato paste into the sauce. Correct seasoning, to taste. Keep warm until needed.
For the Veal: Season the veal with the salt and pepper and sear in a saute pan over high heat. Transfer to a preheated 350 degree F. oven and cook until medium rare (5 to 6 minutes). Remove from oven and keep warm.
Steam the lobsters for 5 to 7 minutes, remove from water, and let rest for 4 minutes. Remove the meat from the shell, slice the tail in half, and keep in a little warm butter until ready to serve.
Steam the cleaned asparagus until slightly underdone. Place a 4-ounce scoop of the artichoke puree in the center of each of 4 plates. On the puree place the veal and lobster so that they cover the puree. Place the warm asparagus on top of the 2 items. Drizzle 3 ounces choron sauce on top of each of the lobsters and around each plate. Garnish with the tarragon sprig.