Bring a large pot of salted water to a boil. Cook fettuccine according to package instructions, around 8-10 minutes. Reserve a cup of pasta water, then drain.

Heat a skillet over medium-high heat, add olive oil. Season chicken breasts, and cook for 6-7 minutes on each side until golden and cooked through. Rest and slice.

In the same skillet, add minced garlic and sauté for 1-2 minutes until fragrant. Add heavy cream and simmer for 3-4 minutes until slightly thickened.

Stir in grated Parmesan and nutmeg, mixing until smooth. Adjust seasoning with salt and pepper.

Add drained fettuccine to the skillet with the Alfredo sauce. Toss for 1-2 minutes, adding reserved pasta water if necessary for desired consistency.

Fold in fresh spinach or steamed broccoli during the last minute of cooking. Mix well.

Plate and garnish with additional Parmesan and black pepper. Serve immediately.