To prepare the sauce, melt butter over medium heat. Add all-purpose flour, stirring until blended. Continue stirring for 3 minutes. Remove pan from the heat.
Add milk and cream and whisk until well-blended. Return pan to medium heat. Heat mixture, stirring frequently until temperature reaches 200°F The mixture will just begin to bubble up the sides of the pot. When the mixture reaches 200° F, remove from the heat and add the 6 tablespoons of Parmesan and 3 tablespoons of Cajun seasoning.
Sprinkle chicken breasts with the Cajun seasoning. Grill for 6 to 8 minutes, or until an internal temperature of 165° F is reached.
Pour 4 cups of Cajun Cream Sauce into a large saute pan. Add linguini and toss with tongs until pasta is evenly coated with the sauce. Cook over medium heat for about 30 seconds.
Divide pasta among 4 large serving plates or bowls, mounding up pasta. Slice cooked chicken on the bias into 1/4-inch strips and place on top of pasta. Sprinkle tomatoes, green onions and Parmesan over each portion. Add garlic toast and serve.