The Brussels sprouts can be prepared through step 2 up to a day ahead. To store them, once they've been well drained, line a storage container with paper towels, place the sprouts in the container and refrigerate. They can then be cooked through while the turkey rests.
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.