Cook the fettuccine pasta according to package directions until al dente. Add broccoli florets to the pasta water during the last 3 to 4 minutes of cooking. Drain and set aside, reserving 1/2 cup pasta water.

While pasta cooks, heat olive oil in a large skillet over medium-high heat. Season chicken pieces with salt and pepper.

Add chicken to the hot skillet and cook for 5 to 7 minutes, turning occasionally, until golden brown and cooked through to internal temperature 165°F. Remove chicken from skillet and set aside.

In the same skillet, reduce heat to medium. Add butter and let it melt.

Add minced garlic and saute for 30 to 60 seconds until fragrant but not browned.

Pour in heavy cream and bring to a gentle simmer. Cook for 2 to 3 minutes, stirring occasionally, until slightly thickened.

Reduce heat to low and stir in freshly grated Parmesan cheese. Stir continuously until cheese melts and sauce is smooth.

Add the pinch of nutmeg if using. Season with salt and black pepper to taste.

Return cooked chicken to the skillet along with the drained pasta and broccoli. Toss everything together until well coated with sauce.

If sauce is too thick, add reserved pasta water a tablespoon at a time until desired consistency is reached.

Garnish with fresh parsley and additional Parmesan cheese if desired. Serve immediately.