Boil fettuccine noodles in a large pot of salted water until cooked to desired tenderness. Drain pasta, reserving 1-2 cups of the pasta water if needed for the alfredo sauce.
Meanwhile, prepare the chicken. Heat grill to 400°F. Pat chicken breasts completely dry. Drizzle with olive oil and sprinkle with salt, pepper, and 1 teaspoon Italian seasoning.
Grill chicken breasts for 4-5 minutes on each side, until internal temperature registers 165°F. Remove from the grill and let rest at least 5 minutes before slicing.
To make the Alfredo sauce, melt butter in a skillet over medium heat.
Add the minced garlic and saute for about 1 minute until fragrant.
Sprinkle the flour over the butter and garlic and saute an additional 1 minute until combined and bubbly.
Slowly whisk the cream and milk into the flour mixture, until a smooth sauce forms. Bring to a low simmer. Add remaining teaspoon of Italian seasoning and then the Parmesan cheese, one handful at a time, and stir until smooth. Remove from heat. Season with salt and pepper, if desired.
Toss cooked fettuccine with the Alfredo sauce, using the reserved pasta water to loosen the mixture and thin the sauce as needed.
Serve with sliced chicken breasts and a garnish of chopped parsley.
Notes
Storage: Store in an airtight container in the refrigerator for 3-4 days.Notes: Thin-sliced chicken breasts will cook more evenly and quickly on the grill. You can substitute your favorite grilled chicken recipe.You can brown the chicken in a skillet (cook until internal temp reaches 165°F) instead of grilling.The Alfredo sauce is a thick, rich sauce. I like to thin with the pasta water - the pasta water works well because it is already salted and it has the starches from the pasta so it maintains a good texture for the sauce.