It's remarkably similar to that Italian staple of pub fayre, lasagne. Well, it would be remarkably similar if it contained tomatoes, herbs, meat and bechamel sauce. As it is, all it is flat pasta (which was a common British dish until the arrival of the potato) and cheese:
"Take good broth and do in an erthen pot. Take flour of paynedemayn and make erof past with water and make erof thynne foyles as paper with a roller; drye it harde and see it in broth. Take chese ruayn grated and lay it in dishes with powder douce and lay eron loseyns isode as hoole as you myght and above powdour and chese; and so twyse or thryse & serue it forth."
In a Telegraph article, Antonio Carluccio is quoted as saying "This sounds a bit far fetched to be called lasagne. But I wouldn't mind making it."