Mix the olive oil, lemon juice, and Cajun seasoning together. Toss the diced chicken through the marinade and leave to marinade for at least 20 minutes.
In a casserole dish, sauté the chicken pieces over medium heat until golden brown and cooked through. Remove from the pan and set aside.
In the same pan, add the onion, celery, and peppers. Cook for 8-10 minutes until softened. Add the garlic and cook for another 2 minutes.
Add tomato paste, chopped tomatoes, and chicken stock when the vegetables have softened. Bring to a boil, then reduce to a gentle simmer. Cook until the sauce has reduced and thickened, at least 10 minutes.
While the sauce simmers away, bring a pan of salted water to the boil. Add the pasta and cook for 10-12 minutes until al dente. Drain and set aside.
When the sauce has thickened, stir in the cream cheese. Then, stir the chicken and pasta through the sauce.
Spoon the pasta into pasta bowls and sprinkle with the parmesan and fresh parsley.