Excellent balsamic vinegar, for drizzling (optional)
In a medium bowl, toss the Parmigiano-Reggiano cheese with 2 tablespoons of the flour. Heat a 10-inch nonstick skillet over moderate heat and lightly dust with flour. Sprinkle 1 tablespoon of the cheese into a 4-inch round in the skillet. Repeat to make 2 more rounds. Cook until the rounds are set and lightly browned around the edges, about 30 seconds. Turn the frico and cook for about 10 seconds longer, then carefully transfer to a plate to cool. Repeat to cook the remaining frico in a single layer, lightly dusting the pan with more flour as necessary.
Cut the pear into thin slices. Fan the slices on the frico and top with a few drops of balsamic vinegar. Arrange on a platter and serve at once.
The frico can be kept in an airtight container for up to 1 day.