01 - Preheat the oven to 400°F. Lightly grease a baking dish with butter or non-stick spray.
02 - Season the chicken breasts evenly on both sides with salt, pepper, and dried thyme.
03 - In a large skillet over medium heat, melt the butter. Add the onion and garlic, sautéing for 2 to 3 minutes until softened and fragrant.
04 - Add the sliced mushrooms to the skillet. Cook for 5 to 6 minutes, stirring occasionally, until golden brown and all released liquid has evaporated.
05 - Sprinkle the flour evenly over the mushroom mixture. Stir continuously and cook for 1 minute to eliminate the raw flour taste.
06 - Gradually pour in the chicken broth and heavy cream, stirring constantly to prevent lumps. Simmer for 2 to 3 minutes until the sauce thickens slightly.
07 - Stir in half of the mozzarella and all of the Parmesan cheese. Continue stirring until fully melted and smooth. Remove the skillet from heat.
08 - Arrange the seasoned chicken breasts in the prepared baking dish in a single layer. Pour the mushroom-cheese sauce evenly over the chicken, ensuring full coverage.
09 - Sprinkle the remaining mozzarella cheese evenly across 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 the oven and let rest for 5 minutes to allow the sauce to set. Garnish with chopped fresh parsley before serving.