Preheat oven to 375°F (190°C).

In a large skillet over medium heat, add olive oil. Once hot, add sliced mushrooms and sauté until golden brown and have released their moisture, about 5-7 minutes.

Add minced garlic to skillet and cook for 1-2 minutes until fragrant, stirring to avoid burning.

In a large mixing bowl, combine cooked chicken, sautéed mushrooms and garlic, heavy cream, dried thyme, oregano, salt, and pepper. Mix until well combined.

Transfer mixture into a greased 9x13-inch casserole dish, spreading evenly across the bottom.

Sprinkle shredded mozzarella and grated Parmesan cheese generously on top of chicken mixture.

Place casserole in preheated oven and bake for 25-30 minutes, or until cheese is bubbly and golden brown.

Remove from oven and let cool for a few moments. Garnish with freshly chopped parsley before serving.