01 - Bring a large pot of salted water to a boil. Cook fettuccine according to package instructions until al dente. Reserve 1/2 cup pasta water, then drain and set aside.
02 - Season chicken strips evenly with salt and black pepper.
03 - Heat olive oil in a large skillet over medium-high heat. Add chicken strips and cook for 5 to 7 minutes, turning occasionally, until golden brown and cooked through. Remove from skillet and keep covered.
04 - Melt butter in the same skillet over medium heat. Add minced garlic and sauté for 1 minute until fragrant without browning.
05 - Pour in heavy cream and whole milk, stirring to combine. Bring to a gentle simmer without boiling.
06 - Gradually whisk in grated Parmesan cheese until the sauce is smooth and thickened, approximately 3 to 4 minutes. Stir in nutmeg if using, and season with salt and pepper to taste.
07 - Return the cooked chicken to the skillet, add the drained fettuccine, and toss gently to coat with the sauce. Add reserved pasta water incrementally if the sauce needs loosening.
08 - Plate immediately, garnished with chopped parsley and additional grated Parmesan cheese.