Preheat your Blackstone griddle to medium heat and drizzle with olive oil.
Add the sliced bell peppers and chopped onion to the griddle. Season lightly with salt and pepper and toss to coat in the oil. Cook until softened and lightly caramelized, using a griddle dome if needed to help them steam and tenderize.
While the vegetables cook, crack the eggs into a bowl. Season with salt and pepper and whisk until fully combined.
Lower the griddle heat to low and pour the eggs directly over the peppers and onions. Gently fold and scramble until the eggs are just set.
Lay the cheese slices over the egg mixture and allow them to melt. Fold gently to distribute the cheese evenly throughout.
Split the Italian rolls and warm them on the griddle until soft and lightly toasted.
Spoon the pepper and egg mixture onto each roll and serve hot.
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