01 - Preheat oven to 400°F. Lightly grease a baking dish with butter or cooking spray.
02 - Season chicken breasts evenly on both sides with salt, pepper, and dried thyme.
03 - In a large skillet over medium heat, melt the butter. Add onion and garlic; sauté for 2–3 minutes until softened and fragrant.
04 - Add sliced mushrooms to the skillet and cook until golden brown and all released liquid has evaporated, about 5–6 minutes.
05 - Sprinkle flour over the mushroom mixture. Stir continuously and cook for 1 minute to form a roux.
06 - Gradually pour in chicken broth and heavy cream, stirring constantly. Bring to a gentle simmer and cook until slightly thickened, 2–3 minutes.
07 - Stir in half of the mozzarella and all of the Parmesan cheese until fully melted and smooth. Remove skillet from heat.
08 - Arrange seasoned chicken breasts in the prepared baking dish. Pour the mushroom-cheese sauce evenly over the chicken.
09 - Sprinkle the remaining mozzarella cheese over the top of the casserole.
10 - Bake for 30–35 minutes until chicken is cooked through (internal temperature reaches 165°F) and the top is bubbly and golden brown.
11 - Remove from oven and let rest for 5 minutes. Garnish with chopped fresh parsley before serving.