1. Boil and drain the fettuccine pasta according to the package instructions. Ensure it's cooked al dente, and avoid overcooking.
2. Sprinkle the chicken pieces with 1 and a half teaspoons of Cajun seasoning and toss to coat evenly. Heat 1 tablespoon each of olive oil and butter in a large skillet over high heat. Place half the chicken in a single layer in the skillet. Avoid stirring. Let the chicken brown on one side for a minute, then flip and cook for another minute. Remove from the skillet with a slotted spoon and set aside.
3. Repeat the above process with the remaining chicken. Remove all chicken from the pan, maintaining high heat.
4. Add the remaining olive oil and butter to the skillet. Once hot, add the peppers, onions, and garlic. Season with the remaining Cajun seasoning and salt if needed. Cook over high heat for a minute, gently stirring to achieve a deep color on the vegetables. Stir in the tomatoes and continue cooking for 30 seconds more. Transfer all ingredients to a clean plate.
5. Deglaze the skillet by adding the wine and chicken broth while on high heat. Continue cooking for 3-5 minutes, scraping the bottom of the pan. Reduce heat to medium-low, then whisk in the cream. Keep whisking and cook over medium-low heat until the sauce thickens slightly. Season to taste with black pepper, cayenne pepper, and more salt if needed. The sauce should have a spicy element to it.
6. Return the chicken and vegetables to the skillet along with any juices that have accumulated on the plate. Stir and cook for 1-2 minutes until heated through. Pour in the drained fettuccine and toss to combine.
7. Finish with chopped fresh parsley as garnish.