Boil pasta in salted water until al dente; reserve some cooking water and drain.
Pat chicken dry, then season with 1 tsp salt, 1/2 tsp pepper, and Italian seasoning.
Heat olive oil in a large skillet over medium-high. Sear chicken until golden and cooked through.
Transfer chicken to a plate. Add butter to the skillet and melt.
Cook mushrooms in butter, stirring occasionally, until browned and their liquid evaporates.
Stir in shallot and garlic; cook until fragrant, about 1 minute.
Sprinkle flour over vegetables; stir for 30 seconds to coat and lightly toast.
Whisk in chicken broth. Simmer until slightly thickened, 2 to 3 minutes.
Lower heat. Stir in cream, Parmesan, lemon juice, and red pepper flakes. Season to taste.
Return chicken and any juices. Toss in pasta, loosening with reserved water as needed.
Finish with parsley and remaining pepper. Serve hot.