Preheat the oven to 375°F (190°C) and lightly grease a 9x13-inch baking dish.
Heat the olive oil in a large skillet over medium heat. Sauté the onion for 3–4 minutes until softened. Add the garlic and cook for 30 seconds.
Stir in the zucchini and cook for another 3–4 minutes until slightly tender. Remove from the heat.
In a large mixing bowl, combine the cooked chicken, sautéed zucchini mixture, sour cream, cream of chicken soup, Italian seasoning, paprika, salt, pepper, 1½ cups cheddar cheese, and Parmesan cheese. Mix until well combined.
Spread the mixture evenly into the prepared baking dish.
In a small bowl, mix the crushed crackers (or panko) with the melted butter and sprinkle evenly over the casserole.
Top with the remaining ½ cup of shredded cheddar cheese.
Bake uncovered for 30–35 minutes, or until the casserole is bubbling and the topping is golden brown.
Let the casserole rest for 10 minutes before serving. Garnish with chopped parsley if desired.