I make a carbonara from a famous "celebrity" chef who many pooh-pooh, but this comes out delicious every time and has no cream (or milk for that matter).

You'll see the name if you google "Bacon and Egg Coal Miner's Pasta" - which actually calls for pancetta, I've used both, but it's the combo of combining the egg yolks, parmesan cheese and pasta water that gives it its thickness.