01 - Bring a large pot of salted water to a boil. Cook the fettuccine according to package instructions. Add broccoli florets during the last 2 minutes. Reserve 1/2 cup of pasta water, then drain and set aside.
02 - Season chicken strips with salt and pepper. In a large skillet over medium-high heat, melt 1 tablespoon butter. Cook chicken until golden and fully cooked, about 5 to 6 minutes. Remove chicken from skillet and keep warm.
03 - In the same skillet, add the remaining 1 tablespoon butter. Sauté garlic until fragrant, about 1 minute. Reduce heat to medium-low, add heavy cream, and bring to a gentle simmer.
04 - Stir in Parmesan cheese, black pepper, and nutmeg. 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 gradually to achieve a silky sauce consistency.
06 - Serve immediately, garnished with chopped parsley and additional Parmesan if desired.