Bring a large pot of salted water to a boil and cook the pasta according to package directions until al dente. In the last 2 minutes of cooking, add the broccoli to the pot to blanch briefly. Drain and set aside.

While the pasta cooks, heat the olive oil in a large skillet over medium-high heat. Season the chicken pieces with salt and pepper, then add to the pan. Cook, stirring occasionally, until the chicken is browned and cooked through, about 6–8 minutes.

Add the minced garlic to the pan and cook for about 30 seconds, until fragrant. Reduce the heat to medium and stir in the butter until melted.

Pour in the heavy cream and bring to a gentle simmer. Stir in the Parmesan cheese, Italian seasoning, and a pinch of nutmeg if using. Let the sauce simmer for 2–3 minutes, stirring frequently, until slightly thickened.

Add the drained pasta and broccoli to the skillet. Toss well to coat everything in the sauce. If the sauce seems too thick, splash in a little milk or some reserved pasta water to loosen it. Taste and adjust with salt and pepper.

Serve immediately, with a little extra Parmesan on top if you like. Leftovers can be stored in an airtight container in the fridge for up to 3 days.