Preheat oven to 375°F (190°C) and grease a 9x13 inch baking dish.
Heat olive oil in a large skillet over medium-high heat. Season chicken with salt, pepper, and onion powder; sear for 5-7 minutes until browned. Transfer chicken to the prepared baking dish.
Melt butter in the same skillet. Add sliced mushrooms and sauté for 6-8 minutes until moisture evaporates and edges are golden brown.
Add minced garlic and dried thyme to the skillet; cook for 60 seconds until fragrant.
Reduce heat to medium. Pour in chicken bone broth and add cream cheese. Whisk constantly until the cream cheese is fully melted and the sauce is smooth.
Stir in heavy whipping cream and simmer for 2-3 minutes until the sauce thickens slightly.
Pour the mushroom cream sauce over the chicken in the baking dish and toss gently to ensure even coating.
Sprinkle the grated parmesan and shredded mozzarella cheese evenly over the mixture.
Bake for 20-25 minutes until the cheese is golden and the sauce is bubbling.
Remove from oven and let rest for 5 minutes before serving to allow the sauce to thicken.