Boil the pasta: Bring a large pot of salted water to a boil. Cook pasta until just al dente. Reserve 3/4 cup pasta water, then drain. Toss pasta with a drizzle of olive oil to prevent sticking.

Season the chicken: Pat the chicken dry. Toss with 1 tablespoon olive oil, 1 to 1.5 tablespoons Cajun seasoning, and a pinch of salt and pepper.

Sear the chicken: Heat 1 tablespoon olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add chicken in a single layer. Cook 3–4 minutes per side until browned and just cooked through. Transfer to a plate.

Sauté the vegetables: Reduce heat to medium. Add remaining 1 tablespoon butter. Stir in onion and bell peppers with a pinch of salt. Cook 4–5 minutes until softened with a little color. Add garlic and cook 30 seconds until fragrant.

Build the sauce: Sprinkle in 1/2 tablespoon Cajun seasoning. Stir in chicken broth, scraping up browned bits. Let it simmer 1–2 minutes to reduce slightly.

Make it creamy: Pour in heavy cream and bring to a gentle simmer. Add Parmesan and stir until smooth. If the sauce is too thick, add 1/4 cup pasta water at a time until creamy and glossy.

Combine: Return chicken and any juices to the skillet. Add cooked pasta. Toss to coat. Adjust seasoning with salt, pepper, and more Cajun seasoning if desired. Add lemon juice for brightness if using.

Finish and serve: Garnish with chopped parsley or green onions. Serve hot with extra Parmesan.