Cook the rice: Prepare rice according to package directions. Fluff and let it cool slightly so it doesn’t steam the casserole mixture.
Preheat and prep: Heat the oven to 375°F (190°C).
Lightly grease a 9x13-inch baking dish with nonstick spray.
Sauté veggies: In a large skillet over medium heat, warm the olive oil. Add the onion and cook 3–4 minutes until translucent. Stir in the garlic for 30 seconds, then add the diced zucchini and a pinch of salt.
Cook 5–7 minutes until tender and most moisture evaporates. If using spinach or bell pepper, stir them in during the last 2 minutes.
Season the base: Sprinkle Italian seasoning, paprika, black pepper, and another small pinch of salt over the veggies. Stir well and remove from heat.
Mix the creamy binder: In a large bowl, whisk the Greek yogurt and chicken broth until smooth.
Stir in half of the shredded cheese and all of the Parmesan.
Combine: Add the cooked chicken, cooked rice, and sautéed veggies to the yogurt mixture. Fold gently until evenly combined. Taste and adjust salt and pepper as needed.
Assemble: Spread the mixture into the prepared baking dish.
Top with the remaining shredded cheese.
Bake: Cover loosely with foil and bake 15 minutes. Remove the foil and bake another 10–12 minutes, until the cheese is melted and the edges are bubbling.
Finish and rest: Let the casserole rest 5–10 minutes so it sets. Sprinkle with fresh parsley or basil before serving.