Preheat oven to 375°F.
In a large bowl, mix cream cheese, sour cream, heavy cream, green chiles, cumin, garlic powder, onion powder, salt, and pepper until smooth.
Stir in shredded Monterey Jack, mozzarella, and shredded chicken until fully combined.
Spread mixture into a greased baking dish.
Top with additional Monterey Jack cheese.
Bake 20–25 minutes until hot and bubbly.
Garnish with fresh cilantro if desired and serve warm.