Preheat and prep: Heat your oven to 375°F (190°C). Grease a 9x13-inch baking dish with butter or nonstick spray.
Sauté aromatics: In a skillet, warm the butter or oil over medium heat.
Add onion and cook 3–4 minutes until softened. Stir in garlic and cook 30 seconds until fragrant.
Mix the sauce: In a large bowl, whisk together the cream of chicken soup, milk, and 2 cups broth. Stir in salt, pepper, paprika, and thyme.
Fold in 1.5 cups of the shredded cheese.
Add the base: If using uncooked rice, stir it directly into the sauce along with the sautéed onions, garlic, vegetables, and chicken. If using cooked rice, reduce the broth to 1/2 cup, then mix everything together gently so the rice doesn’t get mushy.
Adjust liquid: The mixture should look creamy and slightly loose. If it seems too thick with uncooked rice, add up to 1/2 cup more broth.
With cooked rice, it should be thick but spoonable.
Assemble: Spread the mixture evenly in the prepared baking dish. Cover tightly with foil to trap steam if using uncooked rice.
Bake: For uncooked rice, bake covered 35–45 minutes, until the rice is tender and most liquid is absorbed. For cooked rice, bake uncovered 20–25 minutes, until bubbling around the edges.
Top with cheese (and crunch): Remove foil if used.
Sprinkle the remaining 1/2 cup cheese over the top. If you like a crunchy topping, mix crushed crackers or panko with melted butter and scatter it over the cheese.
Finish baking: Return to the oven for 8–12 minutes, until the cheese is melted and the topping is golden. Let the casserole rest 10 minutes to set before serving.
Garnish and serve: Sprinkle with chopped parsley or green onions.
Taste and add a pinch of salt or pepper if needed.