Bring a large pot of salted water to a boil and cook pasta until al dente. Reserve 1/2 cup pasta water and drain. Season chicken evenly with Cajun seasoning, salt, and black pepper. Heat olive oil in a large skillet over medium-high heat. Cook chicken for 5–6 minutes per side until golden and internal temperature reaches 165°F. Remove and let rest before slicing. In the same skillet, sauté sliced bell peppers for 3–4 minutes. Add minced garlic and cook for 30 seconds. Reduce heat to medium and pour in heavy cream and chicken broth. Simmer gently for 4–5 minutes. Gradually stir in Parmesan cheese until melted and smooth. Add reserved pasta water as needed to adjust consistency. Return sliced chicken and cooked pasta to the skillet and toss until evenly coated. Garnish with fresh parsley and serve warm.