Cut beef across the grain into very thin slices. Cut slices so that pieces are no more than 2-inches long. Place on a plate or wide shallow bowl and drizzle with soy sauce. Stir to coat. Set aside.
Tear cheese slices into 1-inch pieces and set aside.
Heat oil in an 11 or 12-inch frying pan. Add onion and slowly brown over medium-high heat for 6-8 minutes. Remove cooked onions from heat and set aside in a bowl.
Add beef to pan. Sauté over high heat 6-7 minutes or until cooked through and liquid is almost gone. Stir in cooked onions.
Remove pan from heat. Distribute the Cooper cheese over beef and stir a bit — the cheese doesn’t have to be totally melted.
Spoon your cheesy Philly-style meat onto the hoagie rolls, then dig in!