Heat the broiler, or have ready a kitchen blowtorch. Cut the cheese in slices ¼ inch (6 mm) thick, and arrange them in a single layer on a rimmed baking sheet. Stir together the sugar and cinnamon. Toast the bread.
Melt the butter in a large, broilerproof frying pan over medium-high heat. Fry the toasted bread, turning once, until crisp and the butter is absorbed, about 1 minute on each