Prep the chicken. Pat the chicken dry and slice large breasts horizontally into cutlets for even cooking. Season both sides with salt, pepper, and a pinch of Italian seasoning.
Sear the chicken. Heat 1 tablespoon olive oil in a large skillet over medium-high.
Add the chicken and cook 3–5 minutes per side until golden and cooked through. Transfer to a plate and tent loosely with foil.
Sauté the mushrooms. Reduce heat to medium. Add the butter and remaining 1 tablespoon olive oil.
Stir in the mushrooms with a pinch of salt. Cook, stirring occasionally, until they release their moisture and turn golden, about 6–8 minutes.
Add garlic and seasoning. Stir in the minced garlic, red pepper flakes (if using), and another pinch of Italian seasoning. Cook 30–60 seconds until fragrant.
Deglaze with broth. Pour in the chicken broth.
Scrape up browned bits from the bottom of the pan. Simmer 2–3 minutes to reduce slightly.
Make it creamy. Lower the heat and stir in the cream (or half-and-half). If you want a thicker sauce, whisk 1–2 teaspoons flour or cornstarch into a splash of cold broth first, then stir into the pan.
Simmer gently for 2–3 minutes.
Melt in the spinach. Add the spinach in handfuls, stirring until wilted. Fold in the Parmesan and a little lemon zest. Taste and adjust salt and pepper.
Return the chicken. Nestle the chicken back into the skillet and spoon the sauce over it.
Warm for 1–2 minutes. Finish with a squeeze of lemon juice and chopped parsley.
Serve. Plate with rice, mashed potatoes, or buttered noodles to soak up the sauce. Add extra Parmesan if you like.