Heat the oven to 400?F.
Heat the olive oil in a large sautÈ pan over medium heat. Add the chopped crawfish and season with Essence. Cook, stirring, for 2 minutes. Add the onions and pepper and season again with Essence. Cook, stirring, for 1 minute. Remove the pan from the heat and stir in 1 tablespoon of the garlic and 1/4 cup of the green onions. Let cool completely.
Rub the ear of corn with the vegetable oil and season with salt and pepper. Put it in a pie tin and roast for 20 minutes, turning the ear every 5 minutes. Remove from the oven, let cool, and, with a sharp knife, cut the kernels from the cob.
In a medium-size mixing bowl, combine the mayonnaise, tomatoes, corn, the remaining 1 teaspoon garlic, and the remaining 2 tablespoons green onions and blend well. Season with salt and pepper. Cover and refrigerate for about 20 minutes.
In a large mixing bowl, combine the flour, baking powder, eggs, and milk and whisk until smooth. Season with salt and pepper, then fold in the crawfish mixture. Stir in the parsley and hot sauce, and cover and refrigerate for 30 minutes.
In a large, heavy, deep pot or electric fryer, heat 4 inches of the vegetable oil to 360?F.
Carefully drop the batter, a heaping tablespoon at a time, into the hot oil. You should be able to do about 6 at a time. Fry the beignets, turning them around in the oil with a spoon, until golden brown, 3 to 4 minutes. Drain on paper towels, then season with Essence.
To serve, spread the tartar sauce in the center of a serving plate. Mound the beignets over the sauce and sprinkle with the chives.
Yield: about 2 dozen