Heat olive oil and butter in a large skillet over medium-high heat.
Add chicken pieces and sauté until browned and cooked through, about 5-7 minutes.
Remove chicken from skillet and set aside.
In the same skillet, add onions, garlic, and bell peppers. Cook until softened, about 5 minutes.
Stir in Cajun seasoning, red pepper flakes (if using), and a pinch of salt and pepper.
Pour in heavy cream and milk, bringing the mixture just to a simmer.
Reduce heat to medium-low and let the sauce thicken, stirring occasionally.
Return cooked chicken to the skillet and stir to coat in the sauce.
Cook for an additional 2-3 minutes until everything is well combined and heated.
Toss cooked pasta with the mixture until evenly coated.
Sprinkle grated Parmesan cheese over the top, if using, and garnish with parsley before serving.