Put the mirliton in a heavy medium pot and cover with water. Bring to a boil and cook until the flesh is tender when pierced with a fork, about 40 minutes. Remove from the heat and drain. Cool, then peel and cut in half. Remove the seed and any stringy membranes surrounding it and cut the halves into 1/2-inch cubes.

Combine the mirliton, tomatoes, red onions, garlic, and parsley in a small bowl. Add the olive oil, salt, and pepper and toss to coat evenly.

Combine the buttermilk and 1 teaspoon of Essence in a large bowl. Add the crawfish tails and let stand for 10 minutes.

Combine the remaining 2 teaspoons of Essence with the cornmeal and masa harina in a shallow bowl.

Remove the crawfish from the buttermilk mixture and add to the cornmeal mixture. Toss to coat evenly, shaking to remove any excess.

Heat the oil in a large, heavy pot or electric fryer to 360?F. Add the crawfish tails, in batches, and cook, turning with a slotted spoon, until golden brown, 1 to 2 minutes. Remove and drain on paper towels.

Divide the salad greens into four equal portions and place on salad plates. Arrange equal amounts of the vegetable mixture on the greens. Top with equal amounts of the crawfish, then drizzle each portion with the remoulade, and sprinkle with cheese. Serve immediately.