Heat the oven to 350°F and grease a deep 9-by-13-inch baking dish with 1 teaspoon of the oil.
Season the beef with 1 teaspoon salt and the pepper, then coat it with the flour and shake off the excess.
Heat the remaining oil in a large skillet over medium-high heat and brown the beef in two batches for about 3 minutes per side.
Spread the rice in the baking dish and arrange the browned beef over it.
Cook the onion, celery and bell pepper in the skillet for 5 minutes, then stir in the tomatoes, broth and remaining salt and bring the mixture to a simmer.
Pour the hot tomato mixture over the beef and rice and cover the dish tightly with foil.
Bake for 90 to 100 minutes, until the rice is tender and the beef is fork-tender and at least 190°F.
Rest the covered casserole for 10 minutes before serving.