This is my grandmother's recipe, as she gave it to me. I have modified it somewhat, as indicated in the footnotes, but either version is excellent. It will be the taste of Thanksgiving to me, now and forever.
Melt butter in a large skillet over medium-high heat. Cook and stir onion and celery in hot butter until tender, about 5 minutes. Stir rice, broccoli, chicken soup, cheese spread, and evaporated milk into the onion mixture; season with salt and pepper. Transfer mixture to a baking dish.
Bake in the preheated oven until rice is tender and sauce is bubbly, about 30 minutes.