Light a gas grill. Set a large cast-iron griddle or very large cast-iron skillet directly on the grill grate and heat it for 10 minutes until very hot.
Meanwhile, in a large bowl, toss the strips of meat with 1 1/2 teaspoons of kosher salt and 1 teaspoon of black pepper.
Brush the griddle with 1 tablespoon of the canola oil. Add the sliced onion and bell peppers and season with kosher salt and black pepper. Cook over high heat, stirring occasionally, until the vegetables are softened and browned in spots, about 8 minutes. Transfer the onion and peppers to a bowl.
Brush the griddle with the remaining 2 tablespoons of canola oil. Spread the meat strips in an even layer on the griddle and cook over high heat, undisturbed, until they are well browned on the bottom, 2 to 3 minutes. Flip the meat and return the vegetables to the griddle. Cook over high heat, stirring occasionally, until the meat is just cooked through, about 3 minutes. Add the torn cheese and cook, stirring, until just melted, 1 minute. Fill each roll with 1 1/2 slices of cheese and the steak-vegetable filling and serve the cheesesteaks immediately.