In a large, heavy pot or an electric fryer, heat the vegetable oil (about 4 inches) to 360ºF.
Using a mandoline fitted with the crisscross blade, cut the potatoes lengthwise into thin wafflelike chips. Fry the potatoes in batches until golden brown, about 2 minutes, then drain on paper towels, and season with salt and pepper. Set aside and keep warm.
In a food processor or blender, combine the egg, both onions, celery, garlic, horseradish, mustard, ketchup, parsley, and lemon juice. Season with salt and pepper and process until smooth. With the machine running, pour the olive oil in a steady stream through the feed tube. The mixture will thicken. Season again with salt and pepper. Toss one-half of the mixture with the lobster meat in a medium-size mixing bowl.
In another medium-size mixing bowl. Toss the greens with the extra virgin olive oil and season with salt and pepper.
To serve, mound the greens in the center of 4 serving plates. Arrange the potatoes around the greens, then top with a spoonful or two of the lobster rémoulade. Garnish with the goat cheese.
The remaining half of the pre-lobster rémoulade can be reserved (refrigerated) and used as a dipping sauce for fried or boiled seafood, or tossed with lump crabmeat.
Yield: 4 servings