In a medium size bowl, whisk the eggs, salt, and Parmesan until well combined.
In a medium size saucepan over medium-high heat, melt the butter and pour the egg mixture into the pan. Let the egg cook just until it starts to set, then add the ham, scallions, and cheddar cheese in the center of the egg wrap.
Cover with a lid and cook for another 3 minutes, or until the egg is fully cooked through and the cheese is melted.
Remove from the pan and fold in the egg wrap’s left and right sides, then roll from the bottom to the top to form a burrito.