Preheat the oven to 400 degrees F.
Cook the Brussels sprouts in a large pot of boiling salted water until softened but not falling apart, about 5 minutes. (Timing will vary depending upon the size of the Brussels sprouts.) Drain well.
Place the oil and garlic in a 9- by 13-inch baking pan and roast until fragrant, about 5 minutes. Add the Brussels sprouts and salt and toss to coat. Toss together the Parmesan, and breadcrumbs in a small bowl and scatter the mixture over the Brussels sprouts. Dot with the butter.
Bake until the crumbs are golden brown and the Brussels sprouts are tender and piping hot, about 15 minutes.