Bucatini Served in a Block of Parmesan

I don't suppose anyone is going to have a half a Parmesan cheese sitting around the house to make this. I've had this, or something very similar in a restaurant. It's very good and very dramatic to have it prepared at your table. The restaurant used a Parmesan wheel cut horizontally through the equator, rather than through a diameter. This seems to me like a better way to do this, since you're going to be tossing a plateful of spaghetti for each serving.