Using a large frying pan or cast iron skillet, heat over high heat.
Add two tablespoons of vegetable oil to pan and add peppers and onions once oil is hot.
Sauté until vegetables are tender but still crisp. Remove from pan and place in a large bowl, set aside.
Heat remaining two tablespoons of oil into pan and heat over medium high heat.
Remove flank steak from baggie and place in the hot pan.
Cook for 5-7 minutes on each side for medium then remove from skillet and place on a cutting board.
Cut against the grain and then cut the steak into small bite-size pieces.
Place steak into large bowl with with the onions and peppers, stir and set aside.
Pour eggs into pan and scramble the eggs over medium heat until done.
Next, add the steak, pepper and onions to the scrambled eggs, stir and top with cheese.
Heat tortillas, and fill each one with the beef fajita mixture, fold burritos and place on a plate until ready to fry.
Heat additional oil in another frying pan or skillet over medium high heat.
Place a few burritos at a time into the hot oil and fry until golden brown on both sides.
Remove fried burritos onto a place lined with paper towels until ready to eat.
Optional: top with salsa, guacamole, cilantro, green onions, sour cream, if desired.