When the pot is too empty for the bread to pick up any cheese, crack an egg inside it and smear it around. Eat it when it turns to omelette (a whole egg, by the way, not just the yolk like I mistakenly said above. I blame the excess of Mumm).

Best way to make sure you don't waste a single bit of cheese :-)

I have definitely seen this done at most of the French and Swiss ski resorts I've been to.