Cook the pasta: Bring a large pot of salted water to a boil. Cook the pasta until just al dente. Reserve 1/2 cup pasta water, then drain and set aside.

Season the chicken: Pat the chicken dry and slice into thin strips. Toss with 1–2 tablespoons Cajun seasoning, a pinch of salt, and a little black pepper.

Sear the chicken: Heat 1 tablespoon olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add the chicken in a single layer and cook 4–6 minutes, stirring once, until browned and cooked through. Transfer to a plate and tent with foil.

Sauté the vegetables: Add the remaining oil and butter to the same skillet. Add peppers and onion with a pinch of salt. Cook 4–5 minutes until softened and lightly charred at the edges. Stir in the garlic and cook 30 seconds, just until fragrant.

Build the sauce: Sprinkle in 1 tablespoon Cajun seasoning. Pour in the chicken broth, scraping up browned bits from the pan. Simmer 2 minutes to reduce slightly.

Make it creamy: Lower the heat to medium. Stir in the heavy cream and bring to a gentle simmer. Let it bubble for 2–3 minutes until slightly thickened.

Add the cheese: Stir in the Parmesan until melted and smooth. Taste and adjust seasoning. If you want more kick, add a pinch of red pepper flakes or an extra shake of Cajun seasoning.

Combine: Return the chicken and any juices to the skillet. Add the cooked pasta and toss to coat. If the sauce is too thick, loosen with a splash of reserved pasta water until glossy and silky.

Finish and serve: Squeeze in a little lemon juice for brightness (optional). Top with chopped parsley or green onions. Serve hot with extra Parmesan on the side.