Preheat an oven to 400ºF.
In a small bowl, combine the Parmigiano and the flour.
On a large nonstick baking sheet, place about 2 tablespoons of the grated cheese in circles about 4 inches across. Place the baking sheet into the oven until they start to smell nutty and the cheese is melted and golden brown, about 10 minutes.
Once the cheese is golden, remove the tray from the oven. Working quickly, lift up the cheese rounds with a small knife or spatula and press them into the cups of an egg carton with your fingers to shape them into small bowls. Let cool.