Prep the chicken: Pat chicken dry. Pound thicker pieces to even thickness, about 1/2–3/4 inch.
Season both sides with salt and pepper. Lightly dredge in flour, shaking off excess.
Sear for color: Heat olive oil in a large skillet over medium-high. Add chicken and cook 4–5 minutes per side until golden and almost cooked through.
Transfer to a plate and tent with foil.
Build the mushroom base: Lower heat to medium. Add butter. Once melted, add mushrooms in an even layer with a pinch of salt.
Cook undisturbed 2–3 minutes to brown, then stir and continue 4–5 minutes until deep golden and any liquid has evaporated.
Add aromatics: Stir in shallot and cook 1–2 minutes until soft. Add garlic and cook 30–45 seconds until fragrant. Don’t let it brown.
Deglaze: Pour in chicken broth.
Scrape up browned bits from the pan. Simmer 2–3 minutes to reduce slightly.
Creamy finish: Stir in cream, Dijon, and thyme or rosemary. Bring to a gentle simmer.
If using Parmesan, add now and stir until melted. Taste and season with salt and pepper.
Return chicken to pan: Nestle chicken into the sauce with any juices. Simmer 3–5 minutes until chicken is cooked through (internal temp 165°F/74°C) and sauce is silky and slightly thickened.
Brighten and serve: Stir in lemon juice to taste.
Sprinkle with parsley. Serve hot over mashed potatoes, rice, buttered noodles, or with crusty bread.