Cook fettuccine in salted water according to package directions just until al dente. Reserve 1/3 cup pasta water then strain and set aside.
Chicken: In a small bowl, mix 2 teaspoons Cajun seasoning with 1 tablespoon olive oil and rub evenly all over chicken breasts. Let chicken sit while you slice your vegetables.
Heat one tablespoon olive oil in a large non-stick skillet over medium-high heat. Once very hot, add chicken and cook, undisturbed for 3-5 minutes, or until nicely browned (or blackened if you prefer) on one side. Turn chicken over, cover, and reduce heat to medium. Cook for approximately 5-7 more minutes (depending on the thickness of chicken), or until chicken is cooked through. Remove to a cutting board and let rest at least 5 minutes before slicing.
Peppers: Add enough olive oil to remaining oil in the pan over medium-high heat. Add peppers, onions and ½ teaspoon Cajun seasoning and saute for one minute. Remove to a plate.
Sun-Dried Tomato Alfredo: Wipe out the skillet and heat 2 tablespoons sun-dried tomato oil over medium heat. Add sundried tomatoes and garlic and saute for one minute. Sprinkle in flour and continue to cook for 2 minutes, stirring constantly.
Turn heat to low and stir in chicken broth. Whisk cornstarch with milk and add to pan along with tomato paste, ½ teaspoon Cajun seasoning, salt, and pepper. Bring sauce to a simmer and continue to cook and stir until sauce is thickened (but not overly thick), approximately 5 minutes.
Reduce heat to low and stir in cream cheese until melted, followed by Parmesan cheese until melted and finally whisk in mozzarella until melted. Add pasta, peppers and toss evenly to coat, adding the desired amount of reserved pasta water a little at a time to reach desired consistency. Top pasta with chicken or toss chicken with pasta.
Garnish individual servings with plenty of freshly squeezed lime juice, salt and pepper. Garnish with fresh parsley if desired. If you like it spicier, sprinkle a little cayenne dusting over top (I always do this – LOVE).