Polenta, or cornmeal, is a staple food in Italy. I once had a waiter tell me that this was an ancient traditional meal, (antico) and I didn’t have the nerve (or the Italian) to point out that corn and tomatoes are from the New World. In any case, it’s Italian enough now.
So this dish is pretty much a lasagna without any lasagne, and without any meat.
You need a packet of quick-cook polenta so that you can make some polenta squares. As for the cheese, any variety called “Swiss” is perfect for this dish. Swiss cheese is basically any cheese with holes in it but the tastiest is Jarlsberg. Emmantal is another idea or, if you’re not short of pennies, use Gruyere. Serve with fresh basil thrown in pieces over the top