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 an even layer and sear for 4 to 5 minutes per side until deeply golden and cooked through. Transfer to a plate and tent loosely with foil to keep warm.
03 - Reduce the heat to medium. Melt the butter in the same skillet, scraping up any browned bits from the chicken. Add the finely 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. Gradually whisk in the freshly grated Parmesan cheese, a handful at a time, until fully melted and the sauce is silky smooth. If the sauce seems too thick, loosen it with small splashes of the reserved pasta water until it reaches your preferred consistency. Sprinkle in the dried Italian herbs if using.
05 - Add the cooked pasta and seared chicken to the skillet, tossing everything together so every strand or piece is thoroughly coated in the creamy garlic Parmesan sauce. Taste and adjust the seasoning with additional salt and pepper as needed.
06 - Transfer to warm serving bowls or plates immediately. Finish with a scatter of chopped fresh parsley and an extra shower of Parmesan if desired. Serve alongside a crisp green salad or crusty bread.