01 - Preheat oven to 400°F. Lightly grease a 9x13 inch baking dish with butter or cooking spray.
02 - Pat chicken breasts dry and season both sides evenly with salt, black 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 to prevent lumps. Simmer for 2 to 3 minutes until the sauce coats the back of a spoon.
07 - Stir in half of the mozzarella and all of the Parmesan cheese into the sauce until fully melted and smooth. Remove skillet from heat.
08 - Arrange seasoned chicken breasts in a single layer in the prepared baking dish. Pour the mushroom-cheese sauce evenly over the chicken, ensuring full coverage.
09 - Scatter the remaining mozzarella cheese over the top of the casserole in an even layer.
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 to allow the sauce to set. Garnish with freshly chopped parsley before serving.