Prep the chicken: Pat the chicken dry. If using breasts, slice horizontally to make cutlets or pound to 1/2-inch thickness. Season both sides with salt and pepper.

Dredge: Place the flour in a shallow dish. Lightly coat each piece of chicken, shaking off excess. This helps develop a golden crust and slightly thickens the sauce later.

Brown the chicken: Heat the olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Sear chicken 3–4 minutes per side until golden and mostly cooked through. Transfer to a plate; tent with foil.

Sauté the mushrooms: Add the remaining 1 tablespoon butter to the skillet. Add mushrooms with a pinch of salt. Cook, undisturbed, for 2 minutes to get color, then stir and cook 4–5 minutes until browned and their moisture evaporates.

Add aromatics: Stir in shallots and cook 1–2 minutes until soft. Add garlic and cook 30 seconds until fragrant. Avoid burning the garlic.

Deglaze with Marsala: Pour in the Marsala wine. Scrape up browned bits from the pan. Simmer 2–3 minutes to reduce slightly and cook off the sharp alcohol edge.

Build the sauce: Add chicken broth, thyme, and Dijon if using. Bring to a gentle simmer. Taste and adjust salt and pepper. For a richer sauce, reduce by about one-third, 4–6 minutes.

Finish with cream: Stir in heavy cream and return to a low simmer. The sauce should be glossy and lightly thickened. If too thin, simmer another minute; if too thick, add a splash of broth.

Return chicken to the skillet: Nestle chicken into the sauce with any accumulated juices. Simmer 2–4 minutes until the chicken is cooked through (internal temp 165°F/74°C) and the sauce coats a spoon.

Garnish and serve: Sprinkle with chopped parsley. Serve with lemon wedges if desired. Pair with mashed potatoes, buttered noodles, polenta, or crusty bread.