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 - Pat the sliced chicken breasts dry and season both sides generously with salt and freshly ground black pepper. Heat olive oil in a large skillet over medium-high heat until shimmering. Arrange the chicken in an even layer and sear without disturbing for 4 to 5 minutes per side until deeply golden and cooked through. Transfer the chicken to a plate and tent loosely with foil to keep warm.
03 - Reduce the heat to medium. In the same skillet, melt the butter, scraping up any browned bits from the bottom. Add the chopped onion and sauté for about 2 minutes until softened and translucent. Stir in the minced garlic and cook for 1 minute until fragrant, being careful not to let it brown.
04 - Pour in the heavy cream and whole milk, stirring to combine. Bring the mixture to a gentle simmer, then gradually whisk in the freshly grated Parmesan cheese a handful at a time until fully melted and the sauce is velvety smooth. If the sauce is too thick, loosen it with small splashes of the reserved pasta water until the desired consistency is reached. Sprinkle in the dried Italian herbs if using.
05 - Return the seared chicken to the skillet along with the drained pasta. Toss everything together, coating the pasta and chicken evenly in the rich sauce. Taste and adjust the seasoning with additional salt and pepper as needed.
06 - Divide among warmed plates or shallow bowls immediately. Garnish each portion with chopped fresh parsley and an extra shower of grated Parmesan if desired. Serve alongside a crisp green salad or crusty bread.