Cook pasta in boiling water until al dente. Reserve 1 cup pasta water. Drain.
Season chicken with salt, pepper, and Italian seasoning. Sear in butter + olive oil until golden and cooked through. Rest, then slice.
In the same skillet, sauté garlic in butter. Stir in cream, milk, & then Parmesan cheese and whisk it prefectly until you get the smooth texture. Season to taste.
Add pasta and chicken back into the sauce. Toss until coated, using pasta water to adjust thickness.
Garnish with parsley and extra Parmesan. Serve hot.