Prep the chicken: Pat dry and season both sides with salt and pepper. If using, lightly dredge in flour, shaking off excess.
This helps create a golden crust and slightly thickens the sauce later.
Brown the chicken: Heat olive oil in a large skillet over medium-high. Add chicken and sear until deeply golden, about 4–5 minutes per side. Transfer to a plate; it will finish cooking in the sauce.
Sauté the mushrooms: Lower heat to medium, add butter.
Stir in mushrooms with a pinch of salt. Cook, undisturbed, for 2–3 minutes to get color, then stir occasionally until browned and their moisture evaporates, about 6–8 minutes total.
Add aromatics: Stir in shallot (or onion) and cook 1–2 minutes until softened. Add garlic and thyme; cook 30 seconds until fragrant.
Avoid burning the garlic.
Deglaze and simmer: Pour in chicken broth, scraping up browned bits. Stir in Dijon, if using. Bring to a gentle simmer and reduce by about one-third, 3–4 minutes.
Make it creamy: Reduce heat to medium-low.
Stir in heavy cream and Parmesan, if using. Simmer 2–3 minutes until slightly thickened and glossy.
Finish the chicken: Nestle chicken back into the skillet with any juices. Simmer gently 4–6 minutes, turning once, until cooked through (internal temp reaches 165°F/74°C).
Add a splash more broth if the sauce gets too thick.
Brighten and serve: Stir in lemon juice. Taste and adjust salt and pepper. Sprinkle with parsley and serve over mashed potatoes, rice, or buttered noodles.