01 - Bring a large pot of salted water to a boil. Cook the fettuccine according to package instructions, adding the broccoli florets in the last 2 minutes. Reserve 1/2 cup of pasta water, then drain and set aside.
02 - Season chicken strips with salt and pepper. Heat 1 tablespoon of butter in a large skillet over medium-high heat. Cook chicken until golden and cooked through, about 5 to 6 minutes. Remove from skillet and keep warm.
03 - In the same skillet, add remaining 1 tablespoon butter. Sauté garlic until fragrant, about 1 minute. Reduce heat to medium-low and pour in heavy cream, bringing it to a gentle simmer.
04 - Stir in grated Parmesan, black pepper, and nutmeg if using. Cook while stirring until the sauce thickens slightly, about 3 to 4 minutes. Adjust salt to taste.
05 - Return chicken, cooked fettuccine, and broccoli to the skillet. Toss to coat evenly, adding reserved pasta water gradually to achieve a smooth sauce consistency.
06 - Plate immediately, garnished with chopped parsley and additional Parmesan as desired.