Place ribeye in the freezer for 15 minutes, remove and shave or slice as thin as possible into strips. The thinner the better.
Whisk eggs and milk together in a bowl and set aside.
On medium high heat drizzle oil and add onion. Cook about 3 minutes or until translucent slide onions to the side to keep warm leaving oil behind.
Turn heat up a bit closer to high heat and add shaved ribeye. Using two spatulas or a scraper to tear apart meat into smaller pieces moving it around constantly for a quick cook, while allowing meat to sear. About 3-5 minutes.
Turn heat to medium low and add onions to mix through. Season with salt and pepper. Spread steak out over the griddle in a large circle and add eggs, turn heat off and gently scramble eggs and meat together. Adding a desired amount of cheese to melt through.
Serve in an Italian hoagie roll or griddle up a griddled sandwich with panini style sourdough bread. Alongside toasted and buttered bread for scooping, Drizzle sriracha ketchup, and enjoy!