Preheat and prep: Heat your oven to 375°F (190°C). Grease a 9x13-inch baking dish with butter or cooking spray.
Par-cook the broccoli: If using fresh, steam or blanch florets for 2–3 minutes until bright green and slightly tender, then drain well.
If using frozen, thaw and squeeze out excess moisture.
Sauté aromatics: In a large skillet, warm olive oil over medium heat. Add chopped onion and cook 3–4 minutes until softened. Stir in garlic and cook 30 seconds until fragrant.
Make the creamy sauce: Add butter to the skillet.
Once melted, sprinkle in flour and whisk for 1 minute to form a smooth roux. Slowly whisk in chicken broth, then milk, until smooth. Simmer 3–5 minutes, stirring, until slightly thickened.
Season and add cheese: Stir in salt, pepper, paprika, onion powder, and garlic powder.
Off the heat, add 1 1/2 cups shredded cheddar and the Parmesan. Stir until melted and silky.
Finish the base: Stir in sour cream or Greek yogurt until the sauce is creamy and smooth.
Combine the casserole: In a large bowl, mix cooked rice, chicken, and broccoli. Pour the sauce over and fold together until everything is well-coated.
Assemble: Transfer the mixture to the prepared baking dish.
Top with remaining 1/2 cup cheddar.
Optional crunchy topping: Mix crushed crackers or panko with melted butter. Sprinkle evenly over the cheese layer.
Bake: Bake uncovered for 20–25 minutes, until bubbly around the edges and the top is lightly golden.
Rest and serve: Let the casserole sit for 5–10 minutes so it sets. Garnish with chopped parsley and serve warm.