Heat oven to 375°F. Lightly grease a 9x13-inch baking dish.
Season chicken with salt, pepper, garlic powder, and onion powder.
Warm olive oil in a large skillet over medium-high heat.
Sear chicken until just opaque at the edges, about 4–5 minutes. Do not fully cook.
Whisk soup, milk, and sour cream in a bowl. Stir in half the cheddar and half the Parmesan.
Combine rice, broccoli, and seared chicken in a large bowl. Pour sauce over and toss to coat.
Spread mixture into the dish. Top with remaining cheddar and Parmesan.
Mix panko, melted butter, and paprika. Sprinkle evenly over the casserole.
Bake 20–25 minutes until bubbly and the topping is golden. Rest 5 minutes before serving.