01 - Bring a large pot of salted water to a rolling boil. Cook pasta according to package directions until al dente. Reserve ½ cup of starchy pasta water before draining. Set drained pasta aside.
02 - Pat chicken slices dry and season generously with salt and black pepper on both sides. Heat olive oil in a large skillet over medium-high heat until shimmering. Sear chicken in an even layer 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 - In the same skillet, melt butter over medium heat. Add the chopped onion and sauté for about 2 minutes until softened and translucent. Stir in the minced garlic and cook for 1 additional minute until fragrant, being careful not to let it brown.
04 - Reduce heat to medium-low. Pour in the heavy cream and whole milk, stirring to combine. Bring to a gentle simmer, then gradually whisk in the grated Parmesan cheese a handful at a time until fully melted and the sauce is silky smooth. If the sauce is too thick, thin it with the reserved pasta water, one tablespoon at a time. Sprinkle in the dried Italian herbs if using.
05 - Slice or shred the rested chicken into bite-size pieces. Add the drained pasta and chicken back into the skillet with the sauce. Toss everything together over low heat until the pasta is evenly coated and the chicken is warmed through. Adjust seasoning with salt and pepper as needed.
06 - Divide among warmed plates or shallow bowls. Finish with a generous sprinkle of chopped fresh parsley and additional grated Parmesan if desired. Serve immediately while hot.