Warm the marinara in a small saucepan over low heat until steaming and thick, about 5 minutes.
Heat the olive oil on a griddle over medium-high heat and cook the onion with 1/4 teaspoon salt for 6 minutes until soft and spotted brown.
Add the shaved beef, remaining salt, oregano and crushed red pepper, then spread it thin and cook for 3 to 4 minutes until browned and at least 145°F.
Chop the beef into bite-size strips, divide it into four piles and place two mozzarella slices over each pile.
Cover the griddle for 45 seconds until the cheese slumps over the meat, then spoon 3 tablespoons marinara across each pile.
Load the rolls immediately and leave the cut sides facing up for 1 minute before closing so excess steam can escape.