Heat a large nonstick skillet. In a small bowl, toss the Parmesan and Asiago cheeses with the flour. Spoon level tablespoons of the cheese mixture at least 2 inches apart into the skillet. Flatten each mound of cheese into a 2 1/2-inch round and cook the rounds over moderate heat until brown around the edges, about 2 minutes. Using a thin spatula, flip the cheese crisps and cook until golden brown. Transfer the crisps to a plate and let cool.
The cheese crisps can be stored in an airtight container for up to 2 days. Recrisp in a hot oven shortly before serving.