Prep the chicken: Pat the chicken breasts dry and pound to about 1/2-inch thickness so they cook evenly. Season both sides with salt and pepper.

Light dredge: Place 1 tablespoon of the flour on a plate. Lightly coat each piece of chicken, shaking off excess. This helps with browning and gives the sauce a little body.

Sear the chicken: Heat the olive oil and butter in a large skillet over medium-high. When hot and shimmering, add the chicken in a single layer. Cook 3–4 minutes per side until golden and just cooked through. Transfer to a plate and tent with foil.

Sauté the aromatics: Lower heat to medium. Add the mushrooms with a pinch of salt. Cook, stirring occasionally, until they release moisture and turn golden, about 6–8 minutes. Add the shallot and cook 1–2 minutes. Stir in the garlic and cook 30 seconds, just until fragrant.

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

Build the sauce: Whisk the remaining 1 tablespoon flour into the chicken broth until smooth, then add to the skillet along with the thyme. Simmer 3–5 minutes, stirring, until the sauce thickens to a glossy, spoon-coating consistency.

Return the chicken: Nestle the chicken and any juices back into the pan. Spoon sauce over the top and simmer 2 minutes to warm through. If you like a hint of brightness, finish with a small squeeze of lemon.

Taste and adjust: Season with salt and pepper as needed. Sprinkle with parsley and serve hot with your favorite sides.