Preheat the oven to 375°F (190°C).
In a large skillet, heat 1 tablespoon of olive oil over medium heat. Add the chopped onion and minced garlic, sauté for 2-3 minutes until fragrant and translucent.
Add the chicken pieces to the skillet. Season with salt, black pepper, dried thyme, dried oregano, and paprika. Cook for 6-8 minutes until the chicken is browned and cooked through. Remove from heat.
In a large pot, bring salted water to a boil. Add the cauliflower florets and cook for 5 minutes until slightly tender. Drain well.
In a large mixing bowl, combine the cooked chicken mixture, cauliflower florets, diced zucchini, chopped spinach, and sliced mushrooms.
In a separate bowl, whisk together the heavy cream and chicken broth.
Pour the cream mixture over the chicken and vegetables. Stir in half of the shredded cheddar and mozzarella cheeses.
Transfer the mixture to a greased 9×13 inch casserole dish. Sprinkle the remaining cheddar and mozzarella cheese evenly on top.
Drizzle the remaining 1 tablespoon of olive oil over the casserole.
Bake uncovered in the preheated oven for 25-30 minutes, until the cheese is melted, bubbly, and golden brown.
Remove from the oven and let the casserole rest for 5 minutes before serving.