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

Blanch the broccoli. In the last 2 minutes of the pasta’s cook time, add the broccoli florets to the pot. Drain together with the pasta. This keeps the broccoli bright and crisp-tender.

Season the chicken. Slice chicken breasts into thin cutlets or bite-size strips. Toss with 1–2 tablespoons Cajun seasoning, 1/2 teaspoon salt, and black pepper until evenly coated.

Sear the chicken. Heat olive oil in a large skillet over medium-high heat. Add chicken in a single layer and cook 3–4 minutes per side until golden and cooked through. Remove to a plate and tent loosely with foil.

Build the sauce base. Reduce heat to medium. Add butter to the same skillet. When melted, add garlic and cook 30 seconds, stirring so it doesn’t brown.

Make it creamy. Pour in heavy cream and 1 teaspoon Cajun seasoning (adjust to taste). Simmer gently for 2–3 minutes, stirring, until slightly thickened.

Add Parmesan. Stir in Parmesan a handful at a time until melted and smooth. If the sauce gets too thick, add splashes of reserved pasta water until it coats the back of a spoon.

Combine. Return chicken (and any juices) to the pan. Add pasta and broccoli, tossing with tongs. Add a squeeze of lemon juice and zest if using. Adjust seasoning with salt, pepper, or more Cajun spice.

Finish and serve. If you like heat, sprinkle red pepper flakes. Top with parsley and extra Parmesan. Serve warm.