01 - Preheat a large griddle or heavy skillet over medium-high heat.
02 - Add 1 tbsp oil to the hot griddle. Sauté onions and bell peppers with a pinch of salt until deeply golden and caramelized, about 8-10 minutes. Transfer to a side of the griddle or a plate.
03 - Add remaining oil to the griddle. Spread sliced ribeye in a single layer. Season with salt and pepper. Cook undisturbed for 1-2 minutes, then stir and cook until just browned, about 3 more minutes.
04 - Return the cooked onions and peppers to the griddle with the beef. Toss everything to combine evenly.
05 - Divide the mixture into 4 equal portions. Place 2 slices of provolone over each portion. Allow cheese to melt completely, about 1 minute.
06 - Split hoagie rolls and butter their insides. Toast buttered sides on the griddle until golden and crispy.
07 - Using a wide spatula, scoop each cheesy beef-onion portion onto a toasted roll. Serve immediately while hot.