01 - Bring a large pot of salted water to a boil. Cook the fettuccine according to package directions. Add broccoli florets during the last 2 minutes of cooking. Reserve 1/2 cup of the pasta water, drain, and set aside.
02 - Season chicken strips with salt and pepper. Heat 1 tablespoon butter in a large skillet over medium-high heat. Cook chicken until golden and fully cooked, about 5 to 6 minutes. Remove chicken from skillet and keep warm.
03 - In the same skillet, melt remaining 1 tablespoon butter. Sauté minced garlic until fragrant, about 1 minute. Reduce heat to medium-low, pour in heavy cream, and bring to a gentle simmer.
04 - Stir in grated Parmesan, black pepper, and nutmeg if using. Cook, stirring constantly, until sauce thickens slightly, about 3 to 4 minutes. Adjust seasoning with salt as needed.
05 - Add cooked fettuccine, broccoli, and chicken to the skillet. Toss to coat evenly, adding reserved pasta water a little at a time to achieve a silky consistency.
06 - Plate immediately, garnishing with chopped fresh parsley and additional Parmesan if desired.