Prepare Chicken: Season the chicken breasts with salt and pepper. Dredge them in flour, shaking off any excess.
Cook Chicken: Heat olive oil in a large skillet over medium heat. Add the chicken breasts and cook until golden brown on both sides, about 3-4 minutes per side. Remove the chicken and set aside.
Prepare Sauce: In the same skillet, add sliced mushrooms and cook until they release their moisture and start to brown, about 5 minutes. Add minced garlic and cook for an additional 1 minute.
Deglaze Skillet: Pour in the Marsala wine and scrape up any browned bits from the bottom of the skillet. Cook for 2-3 minutes until the wine is reduced by half.
Add Broth and Cream: Stir in the chicken broth, heavy cream, and thyme. Bring to a simmer and cook for another 5 minutes until the sauce thickens slightly.
Assemble Casserole: Place the browned chicken breasts in a baking dish. Pour the mushroom sauce over the chicken.
Add Cheese: Sprinkle the Parmesan cheese and shredded mozzarella cheese evenly over the top.
Prepare Breadcrumbs: In a small bowl, combine the breadcrumbs with melted butter. Sprinkle the breadcrumb mixture over the cheese.
Bake: Bake in the preheated oven for 25-30 minutes, or until the chicken is cooked through and the top is golden and bubbly.
Serve: Let the casserole rest for a few minutes before serving. Enjoy!