Whisk the eggs in a mixing bowl until well combined and slightly frothy.
Stir in the shredded cheese until evenly incorporated into the egg mixture.
Preheat the waffle iron until it reaches a hot, steaming temperature, typically indicated by ready lights or a temperature dial set to medium-high.
Lightly grease the waffle iron with non-stick spray or a small amount of oil, then pour half of the cheese-egg mixture onto the center of the lower plate, spreading it lightly if needed.
Close the waffle iron and cook for approximately 3-4 minutes, until the exterior is golden brown and crispy, and the mixture is set and bubbling at the edges.
Carefully open the waffle iron and remove the cooked chaffle with a fork or tongs, then repeat with the remaining mixture. Serve immediately with your preferred toppings.