Cut the chickens in a large heavy pot with 2 tablespoons salt and the cayenne. Add enough water to cover. Bring to a boil, then reduce the heat to medium-low and cook until the chickens are very tender, about 1 hour. Remove the chickens from the pot and reserve 3 cups of the stock. Set aside.

Bring a large pot of water with 1 teaspoon salt and 1 tablespoon olive oil to a boil over high heat. Add the pasta and cook until al dente, about 7 minutes. Remove from the heat, drain, and rinse under cold water. Toss the pasta with the remaining 1/2 teaspoon olive oil and set aside.

When the chicken is cool, remove the meat from the bones, discarding the rest.

Preheat the oven to 350 degrees F.

Combine the butter and flour in a heavy saucepan over medium heat and whisk to blend. Cook, whisking, for 2 minutes. Add the onions and celery and cook, stirring, until just soft, 2 to 3 minutes. Gradually add the reserved chicken stock and whisk to blend. Cook, stirring, until smooth and slightly thickened. Add the chicken and olives and season with the remaining 1 1/2 teaspoons salt, the Essence, and the jalapeÒos. Remove from the heat. Add 1 cup Parmesan and stir to blend.

Spread half of the pasta in a 9 x 13-inch baking dish. Spoon half of the chicken mixture over the pasta and sprinkle with 1/2 cup of the Parmesan. Spread the remaining pasta over the Parmesan and top with the remaining chicken mixture. Sprinkle the casserole with the remaining 1/2 cup Parmesan.

Bake until bubbly and the cheese has melted, about 20 minutes. Remove from the oven and serve warm.