Cook the Chicken: Season the chicken breasts with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Cook the chicken for 5-7 minutes on each side or until golden brown and cooked through. Remove from the skillet and set aside.
Make the Alfredo Sauce: In the same skillet, melt the butter over medium heat. Add the minced garlic and cook for 1-2 minutes until fragrant. Pour in the heavy cream and bring to a simmer. Stir in the grated Parmesan cheese and nutmeg, and cook until the sauce thickens, about 5-7 minutes.
Combine and Serve: Slice the cooked chicken and return it to the skillet. Add the broccoli florets if using. Toss everything to coat with the Alfredo sauce. Garnish with fresh parsley and serve immediately.
