Heat oven to 375°F. Lightly grease a 9×13-inch baking dish.
Make the sauce: In a medium saucepan over low heat, whisk together the condensed cream of chicken soup, sour cream, processed cheese, Dijon, garlic powder, smoked paprika, and black pepper. Warm gently, stirring, until the cheese melts and the mixture is smooth, 3–5 minutes. Remove from heat.
Quick-steam the broccoli: Place the frozen florets in a large skillet with 1/4 cup water. Cover and cook over medium heat until bright green and just tender, 4–5 minutes. Drain well and chop into bite-size pieces.
In a large bowl, combine the cooked rice, diced chicken, chopped broccoli, and dried minced onion. Pour the warm sauce over the top, sprinkle in the kosher salt, and fold until everything is evenly coated. Stir in 1/2 cup of the shredded cheddar.
Spread the mixture into the prepared dish. Top evenly with the remaining 1 cup cheddar.
Cover tightly with foil and bake for 20 minutes. Uncover and continue baking until bubbling at the edges and the cheese is melted, 10–12 minutes. For deeper color, broil 1–2 minutes, watching closely.
Let the casserole rest for 5 minutes before serving so the slices hold together.