Heat the butter in a medium skillet over medium-high heat. Add the onions, bell peppers, and celery. Season with the Essence, salt, and cayenne and cook, stirring, until the onion is slightly soft, about 2 minutes. Add the garlic and cook, stirring, until fragrant, about 30 seconds. Add the flour and cook, stirring until the mixture is lightly golden, about 3 minutes. Add the milk, and continue stirring until the mixture is smooth and thick, about 3 minutes. Remove from the heat. Add the crawfish tails, cheese, green onions, and parsley. Stir to mix well. Remove from the heat and let cool to room temperature.
Preheat the oven to 425?F.
Roll out each pastry sheet to 12 x 15 inches on a lightly floured surface. Trim the edges to make them even. With a sharp knife, cut each sheet into twenty 3-inch squares. Mound about 2 teaspoons of the crawfish mixture in the center of each square, brush 2 edges of the squares with the egg wash, fold over diagonally, and seal. Crimp the edges with a fork. Lightly brush the tops of the turnovers with some of the egg wash. Using the tip of a paring knife, make a tiny slit in the top of each turnover so that steam can escape during baking.
Line a baking sheet with aluminum foil or parchment paper. Place the turnovers about an inch apart on the sheet and bake until golden, 12 to 15 minutes. Remove from the oven and let cool for 5 minutes before serving.
Makes 40 cocktail turnovers, 8 to 10 appetizer servings