1Bring a large pot of salted water to a boil. Add fettuccine and cook until al dente, about 8 minutes. Reserve 1 cup pasta water, then drain and set aside.
2While pasta cooks, heat 2 tbsp butter in a large skillet over medium-high heat. Season chicken with salt and pepper, then add to the skillet. Cook 6–7 minutes, stirring occasionally, until cooked through. Transfer to a plate.
3In the same skillet, melt remaining 4 tbsp butter over medium heat. Add garlic and cook for 30 seconds until fragrant.
4Pour in heavy cream and stir constantly for 2 minutes. Reduce heat to medium-low.
5Gradually whisk in Parmesan cheese until fully melted and smooth, about 3 minutes. If the sauce feels too thick, add reserved pasta water 2 tbsp at a time.
6Return cooked chicken to the skillet. Add drained pasta and toss gently until everything is coated in sauce.
7Season to taste with salt and pepper. Divide among bowls, garnish with fresh parsley, and serve immediately.