01 - Preheat oven to 400°F. Lightly grease a baking dish with butter or non-stick 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, sautéing for 2 to 3 minutes until softened and fragrant.
04 - Add sliced mushrooms to the skillet and cook for 5 to 6 minutes 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 slightly thickens.
07 - Stir in half of the mozzarella and all of the Parmesan cheese until fully melted and smooth. Remove the skillet from heat.
08 - Arrange the seasoned chicken breasts in the prepared baking dish. Pour the mushroom-cheese sauce evenly over each piece of chicken.
09 - Sprinkle the remaining mozzarella cheese evenly over the top of the casserole.
10 - Bake 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 the oven and let rest for 5 minutes. Garnish with chopped fresh parsley before serving.