Whisk eggs, mirin, soy sauce, and salt in a 2-cup measuring glass. Heat oil in a medium nonstick skillet over medium-low. Pour in one third of egg mixture, rotating skillet to evenly distribute. Cook until egg is mostly cooked, about 1 minute. Scatter one third of Parmesan over and shingle 2 seaweed snacks vertically down the center. Using a rubber spatula and starting from one side, fold egg up and over itself to roll up tightly; push to one side. Repeat cooking process with half of remaining egg mixture, Parmesan, and seaweed snacks, then flip existing egg roll over onto flat egg and roll up again. Repeat one more time with remaining ingredients. Transfer gyeran mari to a plate and let cool 5 minutes. Slice into ½"-thick pieces.