Season the chicken breasts generously with salt and pepper. Heat olive oil in a skillet over medium-high heat, then add the chicken and cook until golden brown on both sides and cooked through, about 6-7 minutes per side. Remove from the pan and set aside.
Reduce the heat to medium and add butter to the same pan. Once melted, stir in the minced garlic and sauté until fragrant, about 30 seconds. Watch as it turns golden and releases a warm aroma.
Pour in the heavy cream, stirring continuously to incorporate it with the garlic and butter. Bring the mixture to a gentle simmer, allowing it to thicken slightly, about 3-4 minutes.
Add the grated Parmesan cheese and nutmeg to the skillet. Continue stirring until the cheese melts fully and the sauce becomes smooth and glossy. Adjust seasoning with salt and pepper if needed.
Slice the cooked chicken into thick strips and return to the pan, nestling them into the sauce. Spoon some of the sauce over the chicken and cook for another minute to reheat the chicken, coating it in the creamy sauce.
Serve the chicken and sauce hot, garnished with additional Parmesan or herbs if desired. Enjoy the rich, silky texture and warm, savory flavors of this classic-inspired dish.