Bring a large pot of salted water to a boil. Cook the fettuccine pasta until al dente, about 10-11 minutes. Drain and reserve 1 cup of the pasta water. Set aside.

In a large skillet, melt 1 tablespoon of butter over medium heat. Add the sliced chicken and season generously with salt and pepper. Cook for 5-6 minutes per side until golden and fully cooked. Remove chicken from the skillet and set aside.

In the same skillet, melt the remaining 3 tablespoons of butter over medium heat. Add minced garlic and sauté for 30 seconds until fragrant.

Pour in the heavy cream and reduce heat to low. Simmer gently for 5 minutes, stirring occasionally. Do not boil.

Stir in the grated Parmesan cheese and whisk until smooth and the sauce is thickened, about 2-3 minutes. If the sauce is too thick, gently stir in a small amount of reserved pasta water until desired consistency is reached.

Return the cooked chicken to the skillet and toss to coat in the sauce. Add the drained pasta and mix until everything is evenly coated and heated through, about 2 minutes.

Taste and adjust seasoning with more salt and pepper if needed. Garnish with chopped parsley if using, and serve immediately.