Pre-heat oven to 400°F.

Heat a large non-stick skillet over medium heat. Whisk the eggs in a bowl and pour them in the skillet. Cook the eggs slowly until they just begin to set. Season with salt and pepper as desired. 

Place the eggs, shredded cheese, and ham on the counter where you will be assembling the breakfast burritos.

Unroll the phyllo sheets and cover them with plastic wrap then cover the plastic wrap with a damp towel (this will prevent the phyllo dough from drying out). When you're ready to make the breakfast wraps, remove one or two sheets at a time then cover the sheets of dough you are not working with. 

Place one sheet of phyllo on the counter then brush it with melted butter. Repeat with two more layers of phyllo sheets.

Place a slice of ham at one end of the phyllo sheets then top the ham with some of the scrambled eggs and cheese. 

Fold the sides of the phyllo dough in toward the center and roll the whole thing up into a snug little package. 

Place the rolls on a baking sheet and place in the preheated oven. Bake for 20 to 25 minutes or until golden brown.