Prep & Dredge: Pound chicken to an even ½–¾" thickness. Season with salt and pepper; dredge in flour, shaking off excess.
Sear: In a skillet over medium‑high heat, melt butter with olive oil. Sear chicken 2–3 minutes per side until golden. Transfer to slow cooker.
Assemble: Layer mushrooms, onion, and garlic over chicken. Pour in Marsala wine and broth, then sprinkle thyme, oregano, salt, and pepper.
Cook: Cover and cook on LOW for 5–6 hours (or HIGH for 2½–3 hours) until chicken is tender.
Thicken: Remove chicken and keep warm. Stir cornstarch slurry into sauce, set slow cooker to HIGH, and cook uncovered 15–20 minutes until thickened.
Finish: Stir in heavy cream if using, return chicken to sauce, and warm 5 minutes.
Garnish & Serve: Top with parsley and Parmesan.