Preheat your oven to 375°F (190°C).
In a large skillet, heat the olive oil over medium-high heat. Add the chicken pieces, season with salt and pepper, and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the chopped onion and cook until translucent, about 3 minutes. Add the garlic and mushrooms, and cook until the mushrooms are browned and tender, about 5 minutes.
Stir in the dried thyme, chicken broth, and heavy cream. Bring the mixture to a simmer and let it cook for about 5 minutes, allowing the sauce to thicken slightly.
Return the cooked chicken to the skillet and stir to combine. Transfer the mixture to a baking dish.
Sprinkle the mozzarella and Parmesan cheeses evenly over the top.
Bake in the preheated oven for 20-25 minutes, or until the cheese is bubbly and golden brown.
Remove from the oven and let it cool for a few minutes before serving. Garnish with fresh parsley if desired.

Variations & Tips
For a lighter version, you can substitute the heavy cream with half-and-half or a mixture of milk and Greek yogurt. If you’re a fan of spice, add a pinch of red pepper flakes to the sauce for a little kick. You can also swap out the mozzarella for cheddar or Gruyère for a different flavor profile. For a vegetarian version, replace the chicken with a can of drained chickpeas or some cubed tofu.