Preheat the oven to 375°F (190°C) and lightly grease a 9×13-inch baking dish.
In a large mixing bowl, whisk together the olive oil, chicken broth, heavy cream, paprika, garlic powder, and ground mustard until combined.
Add the frozen peas and carrots, frozen corn, and dry orzo to the bowl and stir to combine.
Stir in 1 cup shredded Cheddar and 1/3 cup grated Parmesan, season with salt and pepper (about 1 tsp each if following the author's amounts), and mix gently until evenly distributed.
Transfer the mixture to the prepared baking dish and press it into an even layer.
Sprinkle the remaining 1/2 cup Cheddar and remaining 1/3 cup Parmesan evenly over the top.
Bake, uncovered, for 40–45 minutes, or until the orzo is tender and the casserole is creamy and set at the edges.
Remove from the oven; add the diced rotisserie chicken, finely diced broccoli, and the remaining 1/2 cup Cheddar, then gently fold them into the hot casserole.
Cover the dish with foil and let it rest for 10 minutes to thicken, then stir gently once more, taste, adjust seasonings if needed, and serve warm.