01 - Bring a large pot of salted water to a rolling boil. Add the pasta and cook according to package directions until al dente. Reserve ½ cup of the starchy pasta water before draining. Set the drained pasta aside.
02 - Season the thinly sliced chicken breasts generously with salt and freshly ground black pepper on both sides. Heat olive oil in a large skillet over medium-high heat until the oil shimmers. Add the chicken in a single layer and sear for 4 to 5 minutes per side until golden brown and cooked through. Transfer the chicken to a plate and tent loosely with foil to keep warm.
03 - In the same skillet, reduce the heat to medium and melt the butter. Add the finely chopped onion and sauté for about 2 minutes until softened and translucent. Add the minced garlic and cook for 1 additional minute, stirring constantly to prevent burning.
04 - Lower the heat to medium-low. Pour in the heavy cream and whole milk, stirring to combine. Bring the mixture to a gentle simmer without boiling. Gradually whisk in the freshly grated Parmesan cheese, allowing each addition to melt smoothly before adding more. If the sauce is too thick, thin it with the reserved pasta water, adding 1 tablespoon at a time until the desired consistency is reached. Sprinkle in the dried Italian herbs if using.
05 - Add the cooked pasta and seared chicken back into the skillet with the sauce. Toss everything together over low heat until the pasta and chicken are evenly coated and heated through. Adjust seasoning with additional salt and pepper to taste.
06 - Divide among serving plates immediately. Garnish with freshly chopped parsley and an extra sprinkle of Parmesan cheese if desired. Serve hot.