Slice each chicken breast horizontally to create 4 thin cutlets. Season both sides with salt and pepper. Dredge lightly in flour, shaking off any excess.

In a large skillet over medium heat, heat olive oil and 1 tablespoon of butter. Add chicken and sear for 3–4 minutes per side until golden and cooked through. Transfer to a plate and cover loosely with foil.

In the same skillet, add the remaining tablespoon of butter. Add the sliced mushrooms and sauté for 4–5 minutes until browned and softened. Stir in the minced garlic and cook for 30 seconds until fragrant.

Pour in the wine (or broth), scraping the bottom of the skillet to release the brown bits. Let it reduce by half, then add lemon juice, capers, and chicken broth. Simmer for 3–4 minutes to allow flavors to meld.

Add the seared chicken back into the sauce. Spoon the sauce and mushrooms over the top and simmer for another 2–3 minutes to heat through.

Sprinkle with chopped fresh parsley and garnish with lemon slices if desired. Serve hot over pasta, mashed potatoes, or rice.