Bring a large pot of salted water to a boil. Add the fettuccine pasta and cook according to package instructions. In the last 3 minutes of cooking, add the broccoli florets. Drain and set aside.

In a large skillet, heat olive oil over medium-high heat. Season the chicken pieces with salt and pepper. Add the chicken to the skillet and cook until golden brown and cooked through, about 5-7 minutes. Remove the chicken and set aside.

In the same skillet, reduce the heat to medium and add the butter. Sauté the minced garlic for 30 seconds until fragrant.

Pour in the heavy cream and let it simmer gently. Gradually add the grated Parmesan cheese, stirring until it melts into a smooth sauce.

Add the cooked pasta, broccoli, and chicken back to the skillet. Toss gently to coat everything in the sauce. If the sauce is too thick, add a splash of pasta water to loosen it.

Season with nutmeg and fresh parsley. Serve hot and enjoy!