Heat the oven to 350°. In a medium saucepan over low heat, warm the broth and milk until just steaming.
Meanwhile, heat the oil in a 12-inch ovenproof casserole or skillet over medium heat. Add the onion and celery. Cook until the onion is soft and translucent, add the flour, and stir constantly for about 2 minutes.
Whisk the milk mixture into the flour, onion, and celery. Add the sour cream and 1 cup of the cheddar and whisk until smooth. Add the rice and stir to combine. Cover the pan with a tight-fitting lid or foil and transfer to the oven. Bake until the rice is tender and the liquid has been absorbed, about 1 hour 15 minutes, stirring once halfway through baking.
Meanwhile, in a covered bowl, microwave the broccoli with 1/4 cup water until just tender. Combine the panko and remaining cheese.
When the rice is tender and the liquid is absorbed, remove the dish from the oven and add the broccoli, reserving 1 cup. Sprinkle on the panko-cheese mixture and the remaining broccoli. Bake, uncovered, until the topping is golden brown, about 15 minutes more. (To make ahead, skip this last baking step and refrigerate or freeze the dish. Reheat the thawed dish covered for 30 minutes, then uncovered for 15 minutes.)