1. Bring a large pot of salted water to a boil and cook the fettuccine according to package instructions. Add the broccoli florets during the last 3 minutes of cooking. Drain and set aside.
2. Meanwhile, heat olive oil in a large skillet over medium-high heat. Season the chicken pieces with salt and pepper, then add them to the skillet. Cook for 5-7 minutes, until golden and cooked through. Remove the chicken from the skillet and set aside.
3. In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant.
4. Reduce the heat to low and pour in the heavy cream, stirring to combine. Let it simmer gently for about 3-4 minutes.
5. Add the grated Parmesan cheese and nutmeg, stirring continuously until the cheese has melted and the sauce is smooth and creamy.
6. Return the cooked chicken and the pasta-broccoli mixture to the skillet, tossing everything together until well-coated in the sauce.
7. Garnish with fresh parsley if desired, and serve hot.

Remember, as my abuela always said, “trust your senses.” Adjust the seasoning to your liking, and don’t be afraid to get a little creative with extra herbs or spices.