While all Philly cheesesteak sandwiches have steak, peppers, cheese and Italian rolls, there isn’t just one way to make them. Some have thinly shaved beef, some sliced beef, some chunks of beef.
Add the ribeyes to a parchment paper-lined baking sheet and freeze for an hour; this will make it easier to thinly slice the beef.
Once chilled, remove the steak from the freezer and thinly slice across the grain. Divide into 8-ounce portions and set aside.
Heat a large sauté pan over medium heat, add the olive oil and heat through. Add the onions and peppers, sautéing until the onions are tender and slightly browned and the peppers are slightly charred, about 12 minutes. Toss with the vinegar, remove from the heat and set aside.
Heat a griddle or medium cast iron skillet over medium heat, add 1 tablespoon of the canola oil and heat through. Working in batches, add 2 portions of the steak (1-pound) to the griddle and cook, moving around with a spatula until almost cooked through, but still partially pink, about 3 minutes.
Season the beef with salt and pepper. Make the meat into a rectangular mound and top with some of the onion and pepper mixture.
Top with 3 slices of the cheese, alternating the American and Provolone, and let cook, undisturbed until the cheese has melted into the meat, about 2 minutes.
Use a spatula to scoop the meat mixture onto the rolls. Close and cut in half. Repeat with the remaining ingredients. Serve hot.