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 cheddar cheese, black beans, onions, and peppers to 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.
Add avocados and remove from the pan. Fold in the egg wrap’s left and right sides, then roll from the bottom to the top to form a burrito.