Preheat the oven to 350 degrees F. Combine the Parmesan cheese, bread crumbs and butter until thoroughly incorporated, and press the mixture into the bottom of a 9-inch springform pan. In a saute pan, heat the olive oil. Add the onions and peppers. Saute for 2 to 3 minutes then remove from heat. In an electric mixer, beat the cream cheese and eggs together until thick and frothy, about 5 minutes. Beat in the cream, cheddar cheese, sauteed vegetables and crawfish. Mix until thoroughly incorporated and creamy, about 2 minutes. Pour the filling over the crust in the springform pan and bake until firm-about 1 hour. Remove from the oven and allow to cool to room temperature.

For the sauce: In a sauce pot, combine all the ingredients together. Bring the mixture up to a boil. Reduce to a simmer and simmer for about 5 to 6 minutes. With a hand -held blender, puree the mixture until smooth. Season with salt and pepper. Spoon the sauce on the bottom of the plate and dirty the rim. Place a wedge of the cheesecake in the center of the sauce. Garnish with the fried crawfish tails, white cheddar cheese, parsley and red onions.