01 - Boil fettuccine in a large pot of salted water until al dente according to package directions. Reserve 1/2 cup pasta water, then drain and set aside.
02 - Season chicken strips with salt and freshly ground black pepper evenly.
03 - Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add the chicken strips and cook 5 to 6 minutes until golden and cooked through, turning occasionally. Remove chicken and set aside.
04 - Reduce heat to medium, add remaining 1 tablespoon butter and minced garlic to the skillet. Cook for 1 minute until fragrant.
05 - Pour in heavy cream and milk, stirring well. Bring mixture to a gentle simmer.
06 - Whisk in Parmesan cheese gradually until the sauce thickens and becomes smooth, about 2 to 3 minutes. Stir in nutmeg if using, then adjust seasoning with salt and pepper.
07 - Return cooked chicken to the skillet. Add drained pasta and toss to coat evenly, adding reserved pasta water as necessary for a silky consistency.
08 - Plate immediately, garnished with chopped parsley and additional Parmesan cheese to taste.