Heat oven to 375°F. Lightly grease a 9x13-inch baking dish.
Combine rice, broth, condensed soup, sour cream, onion powder, garlic powder, thyme, salt, and pepper in the dish.
Fold in peas and carrots, if using, until evenly dispersed.
Pat chicken dry. Toss with a pinch of salt and half the paprika. Nestle the pieces over the rice mixture.
Drizzle melted butter over the top and dust with remaining paprika. Cover the dish tightly with foil.
Bake 40 minutes. Uncover, stir gently to redistribute rice, and sprinkle cheddar on top if using.
Bake 10–15 minutes more, until rice is tender and chicken reaches 165°F. Rest 10 minutes, then garnish with parsley.