Combine the egg yolks, vinegar, mustard, and lemon juice in a food processor and process for 2 minutes. With the processor running, add the oil slowly in a thin stream and process until emulsified.

Remove to a mixing bowl and gently fold in the capers, scallions, and parsley. Season with salt and white pepper. Chill for 2 to 4 hours. Just before serving, gently fold in the crawfish, taking care not to break up the lumps. Divide the lettuce among 6 servings and top with a slice of tomato. Spoon the crawfish on top of the tomato and serve.

Note:  If using leftover crawfish tails from a crawfish boil, the salad should be tasted before any additional seasoning is added.