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 chicken breast slices 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 a single layer and sear for 4 to 5 minutes per side until golden brown and cooked through. Transfer to a plate and tent loosely with foil to keep warm.
03 - Reduce the heat to medium. In the same skillet, melt the butter. Add the chopped onion and sauté for about 2 minutes until softened and translucent. Stir in the minced garlic and cook for an additional 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. 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 seems too thick, loosen it with small splashes of the reserved pasta water until it reaches the desired consistency. Sprinkle in the dried Italian herbs if using.
05 - Add the cooked pasta and seared chicken to the skillet. Toss everything together, coating the pasta and chicken evenly in the rich Parmesan sauce. Taste and adjust the seasoning with additional salt and pepper as needed.
06 - Divide among warm serving plates. Garnish with freshly chopped parsley and an extra sprinkle of grated Parmesan if desired. Serve immediately while hot.