01 - Bring a large pot of salted water to a boil. Cook fettuccine according to package directions until al dente. Reserve 1/2 cup of the pasta cooking water, then drain and set aside.
02 - Season chicken strips with salt and black pepper. Heat olive oil in a large skillet over medium-high heat. Add chicken and cook for 5 to 7 minutes, turning occasionally, until golden brown and cooked through. Transfer to a plate and cover loosely.
03 - In the same skillet, melt the butter over medium heat. Add minced garlic and sauté for 1 minute until fragrant.
04 - Pour in heavy cream and whole milk, stirring to combine. Bring to a gentle simmer without boiling.
05 - Whisk in grated Parmesan cheese gradually until the sauce is smooth and thickened, about 3 to 4 minutes. Stir in nutmeg if desired. Season with salt and black pepper to taste.
06 - Return the cooked chicken to the skillet, add the drained fettuccine, and toss to coat evenly in the sauce. Add reserved pasta water incrementally if the sauce needs thinning.
07 - Serve immediately, topped with chopped fresh parsley and extra grated Parmesan cheese.