Bring a large pot of salted water to a boil. Cook pasta to al dente. Drain, reserving ½ cup of pasta water.
While the water is coming to a boil and the pasta is cooking, chop the chicken into bite sized pieces.
Heat a large heavy bottomed skillet over medium heat. Add the oil and butter and cook until butter has melted.
Season the chicken with half of the Cajun seasoning.
Add the chicken to the skillet and cook, stirring often, until cooked through, about 6-7 minutes. Remove and set aside.
Add the sausage to the skillet along with the peppers. Sprinkle the remaining Cajun seasoning over the top and cook for 5 minutes, stirring often, until the sausage has browned and the peppers have softened. Stir in the garlic and cook for 30 seconds more. Remove from the pan and set aside with the chicken.
Add the cream to the pan and bring to a simmer. Remove from the heat. Add the Parmesan cheese and stir until the cheese has melted.
Return the chicken, sausage, and pepper to the pan along with the cooked pasta. Stir well to coat.
To thin the sauce, add reserved pasta water, a couple tablespoons at a time, until the sauce reaches your desired consistency.
Sprinkle with parsley before serving.