Heat a dash of oil in a frying pan, and add the strips of tortilla. Cook over a medium heat for a few minutes, tossing regularly, until the tortilla pieces are golden brown and crispy. Remove from the pan, and set aside.
Add the diced onion and pepper to the pan, and cook over a medium heat for a few minutes, until fairly soft. Add the diced tomato, and cook for a further couple of minutes.
Return the crispy tortilla strips to the pan, and add the beaten eggs. Cook over a medium-low heat, stirring regularly, until the eggs are almost cooked, then add the grated cheese and plenty of salt and pepper.
When the cheese has melted and the eggs are fully cooked, serve the migas with refried beans, avocado, and slices of red onion.