Dice potatoes and cook them in a large skillet until tender. While potatoes cook, crack and whisk eggs in a separate bowl; set aside. Add chorizo and cook until browned.
Pour in whisked eggs and cook, stirring everything together.
Heat tortillas and store under a towel. Scoop about ½ to ¾ of a cup of potato mixture on tortilla; sprinkle with cheese and roll.
Wrap burritos in aluminium foil and share. Serve with red sauce, sour cream or guacamole.