Preheat the oven to 350 and grease or spray a 9 x13 baking dish. Spread 3 c. cooked rice in an even layer and then place 20 oz. thawed, well-drained broccoli spears over the rice and set aside. . I think spears make a nicer presentation but you can use large-chopped broccoli as well. The really small cuts seem to disappear though. If doubling the recipe or using a smaller dish, feel free to layer the rice, sauce, broccoli & cheese a couple times.
Melt 2 oz butter in a large saucepan, add 1/2 c chopped onion and 1/4 tsp thyme, and cook over moderate heat until onion is tender and you can smell the thyme. Stir in 3 TB flour, then 3 c milk. Cook and stir over medium heat -- watch so it doesn't burn-- until it's thickened and bubbly. Pour the sauce over the rice and broccoli. Top with 8 oz sliced or shredded Swiss cheese, and 1/2 c buttered bread crumbs. Bake uncovered for 45 minutes, until top is golden and sauce is bubbly. Serves 12. For a half-recipe, use an 8" square pan.