Bring a large pot of salted water to a boil. Cook the pasta according to the package directions until al dente. Drain and set aside.

Meanwhile, steam or blanch the broccoli florets for about 3–4 minutes until tender but still bright green. Drain and set aside.

In a large skillet, heat 2 tablespoons of olive oil over medium heat. Season the diced chicken with salt and pepper. Add the chicken to the skillet and sauté for 5–7 minutes, or until browned and cooked through. Remove the cooked chicken from the skillet and set aside.

In the same skillet, add the remaining 1 tablespoon of olive oil. Stir in the minced garlic and sauté for 1–2 minutes until fragrant.

Reduce the heat to low and pour in the heavy cream. Stir in the Parmesan cheese, whisking gently until the cheese is melted and the sauce begins to thicken. If the sauce feels too thick, you can add a splash of reserved pasta water to loosen it. Season with salt and pepper to taste.

Add the cooked pasta, broccoli, and chicken back to the skillet with the creamy sauce. Toss everything together until the pasta is fully coated and heated through. If you’d like a bit of heat, sprinkle in the red pepper flakes.

Transfer the pasta to bowls or plates, garnish with fresh parsley if desired, and serve hot with extra Parmesan on the side.