01 - Preheat oven to 400°F. Lightly grease a 9x13-inch baking dish with butter or nonstick spray.
02 - Pat chicken breasts dry and season both sides evenly with salt, pepper, and dried thyme.
03 - Melt butter in a large skillet over medium heat. Add onion and garlic; sauté for 2 to 3 minutes until softened and fragrant.
04 - Add sliced mushrooms to the skillet and cook for 5 to 6 minutes, stirring occasionally, until golden brown and all released liquid has evaporated.
05 - Sprinkle flour over the mushroom mixture and stir continuously for 1 minute to cook out the raw flour taste.
06 - Gradually pour in chicken broth and heavy cream, stirring constantly. Bring to a gentle simmer and cook for 2 to 3 minutes until the sauce thickens slightly.
07 - Remove skillet from heat. Stir in half of the mozzarella and all of the Parmesan cheese until fully melted and smooth.
08 - Arrange seasoned chicken breasts in the prepared baking dish. Pour the mushroom-cheese sauce evenly over the chicken, ensuring full coverage.
09 - Sprinkle the remaining mozzarella cheese evenly over the top of the casserole.
10 - Bake uncovered for 30 to 35 minutes until the chicken reaches an internal temperature of 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.