Pat chicken dry and season both sides with salt and pepper. If breasts are thick, slice horizontally or pound between plastic wrap to about ¼ inch.

Place flour in a shallow bowl and lightly coat each piece, shaking off excess.

Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Cook chicken in batches, 2–3 minutes per side until golden brown. Transfer to plate and tent with foil.

Reduce heat to medium and add the remaining tablespoon butter. Add mushrooms and a pinch of salt. Cook until they release their liquid and start to brown, about 5–7 minutes.

Push mushrooms to the side, add shallot, and sauté for 1–2 minutes until softened. Then add garlic and cook 30 seconds.

Pour in the Marsala wine, scraping browned bits from the pan. Let it bubble and reduce by about half, 2–3 minutes.

Add chicken broth and fresh thyme, simmer for 3–5 minutes. For richer sauce, stir in the heavy cream and simmer until it thickens, about 2 minutes.

Return chicken to the pan, nestle into the sauce, and simmer gently for 3–4 minutes until chicken reaches 165°F.

Adjust seasoning with salt, pepper, and lemon juice if desired. Sprinkle parsley over top and serve immediately.