Preheat the oven to 400 degrees F and butter a 2-quart baking dish. Bring a large pot of salted water to a boil. Add the Brussels sprouts and cook until tender, 8 to 10 minutes.
Drain the Brussels sprouts and coarsely chop. Transfer to the prepared baking dish and toss with the red pepper flakes, and salt and pepper to taste, then spread out evenly. Pour the cream on top, sprinkle with the cheese and breadcrumbs and dot with the butter pieces.
Bake the gratin until bubbly and golden brown, about 15 minutes.