Steam the broccoli in a pan with 1/2-inch water, over medium heat, until crisp tender. Drain and add to a large bowl. Add the cream of mushroom soup, stuffing mix, and butter and stir to combine. Spread evenly into a 9 by 13-inch ovenproof baking dish. Bake for 30 minutes topping with cheese before last 10 minutes of cooking. Remove from the oven and serve.
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