Heat a medium nonstick skillet over medium heat. Sprinkle about 1 1/2 tablespoons Parmesan on skillet to form a 4-inch round. Cook until Parmesan is somewhat melted and starting to firm, about 3 minutes. Using a thin spatula, flip; cook until firm but not browned, 20 to 30 seconds more. Transfer to a small bowl (about 2 1/2 inches in diameter), and press into bowl to shape. Let cool completely. Repeat with the remaining Parmesan to make 4 frico bowls.