In a saucepan, over medium heat, combine the vanilla bean, pulp and oil. Bring to a simmer and cook for 10 minutes. Remove from the heat, cool completely and strain.
In a food processor, fitted with a metal blade, combine the egg, mustard, tarragon and lemon. Process until smooth. Season with salt and pepper. With the machine running, add 1 cup of the vanilla oil slowly, in a steady stream. Process until the mixture is thick and creamy. Remove and refrigerate for at least 1 hour. Can be made the day ahead of time.
In a mixing bowl, combine the lobster, potatoes, onions, celery and garlic. Season with salt and pepper. Toss well. Fold in the vanilla bean emulsion. Mix well. In another mixing bowl, toss the maiche with the remaining vanilla oil. Season with salt and pepper.
To serve, place the greens in the center of each serving plate. Mound the lobster salad in the center of each plate of greens. Garnish with parsley. Serve the croutons with the salad.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.