01 - Set the oven to 350°F (180°C) to preheat.
02 - Heat olive oil in a large skillet over medium heat. Add finely chopped onion and minced garlic, sautéing for 2 to 3 minutes until fragrant.
03 - Incorporate broccoli florets, diced zucchini, and diced red bell pepper. Cook for 5 minutes, stirring occasionally until slightly tender.
04 - Add shredded chicken, dried thyme, smoked paprika, salt, and black pepper to the skillet. Stir well and remove from heat.
05 - In a medium bowl, whisk heavy cream and softened cream cheese until smooth. Stir in half of the shredded cheddar and mozzarella cheeses until combined.
06 - Pour the creamy cheese mixture into the skillet with chicken and vegetables. Stir thoroughly to coat all ingredients evenly.
07 - Transfer the mixture to a greased 9x9 inch (23x23 cm) casserole dish.
08 - Sprinkle the remaining cheddar and mozzarella cheese evenly over the top of the casserole.
09 - Place the casserole uncovered in the preheated oven and bake for 25 to 30 minutes, until bubbly and golden brown on top.
10 - Allow to rest for 5 minutes to set before serving.