01 - Bring a large pot of salted water to a boil. Add fettuccine and cook according to package directions. Add broccoli florets during the last 2 minutes of cooking. Reserve 1/2 cup pasta water, drain pasta and broccoli, then set aside.
02 - Season chicken strips with salt and black pepper. In a large skillet over medium-high heat, melt 1 tablespoon butter. Cook chicken until golden brown and fully cooked, about 5 to 6 minutes. Remove from skillet and keep warm.
03 - In the same skillet, add remaining 1 tablespoon butter. Sauté minced garlic until fragrant, approximately 1 minute. Reduce heat to medium-low, add heavy cream, and bring to a gentle simmer.
04 - Stir in grated Parmesan cheese, black pepper, and a pinch of nutmeg if using. Cook while stirring until sauce slightly thickens, about 3 to 4 minutes. Adjust salt to taste.
05 - Return cooked fettuccine, broccoli, and chicken to the skillet. Toss to combine thoroughly, adding reserved pasta water gradually to achieve desired sauce consistency.
06 - Transfer to plates and garnish with chopped fresh parsley and additional Parmesan cheese if desired. Serve immediately.