Roast the poblano over medium heat until charred. Place into a bag to sweat it for 10 minutes. Peel, using your favorite method. Slice and chop.
While pepper is sweating, chop up the onion and start a pan over medium heat. Sauté the onion until just soft and add the diced peppers.
In a small bowl, whisk the eggs until fluffy. When the peppers and onions are hot, add eggs and slowly mix together; scraping the eggs from the sides and bottom of the pan, using a folding-stir method.
When eggs look nearly set, add the crumbled tortillas and 1 cup of the cheese and continue folding to mix everything together.
Put the rest of the grated cheese on top and throw a lid on the pan for about 3 minutes.