Remove any excess fat from the steak and cut into bite sized pieces.
Crack the eggs in a bowl and add the milk, kosher salt, and pepper. Whisk until combined.
Preheat the griddle to medium heat and add cooking oil of choice and the steak. Season with kosher salt, pepper, and steak seasoning. Cook 1 to 2 minutes flipping with hibachi spatulas.
Add some cooking oil to the other side of the griddle and slowly pour the eggs, stopping a few times to use the hibachi spatulas to keep the eggs contained so they don't go all over the griddle.
Cook the steak and eggs together for 3 to 4 minutes on the griddle stirring and combining with the hibachi spatulas. Use the spatulas to remove the steak and eggs from the griddle.
Turn the griddle off so the steak and eggs can cool and to allow time for you to make the burritos. To assemble each burrito, place some cheese in the center of each tortilla. Add some steak and eggs, fold the sides in and tightly roll into a burrito.
Place the burritos seam side down on a tray and preheat the griddle to medium. Add some cooking oil, place the burritos seam side down and cook them 1 1/2 to 2 minutes per side.
Put the burritos back on the tray and serve. These can also be wrapped in foil and stored in the freezer. Remove the foil and heat them for a minute or two in the microwave.
Serve with optional toppings such as sour cream, salsa, and/or hot sauce if desired.