Season the Beef
Generously season the sliced ribeye with salt and pepper. Set aside.
Cook the Onions
Place a large skillet over medium heat and melt the butter. Add the sliced onion and cook for 6 to 8 minutes until lightly caramelized.
Add the Peppers
Add the sliced green bell pepper and cook for another 3 to 4 minutes until softened. Season with salt and pepper.
Set Aside Vegetables
Transfer the cooked onions and peppers to a plate and return the skillet to the stove.
Cook the Beef
Increase the heat to medium-high and add the vegetable oil. Add the beef and sear for 3 to 4 minutes until just barely cooked through.
Combine Ingredients
Return the onions and peppers to the skillet and stir until evenly mixed with the beef.
Melt the Cheese (First Layer)
Place 3 slices of provolone over the beef mixture. Add 1–2 tablespoons of water to the side of the skillet, cover, and let steam for 1 minute until the cheese melts.
Melt the Cheese (Second Layer)
Stir the mixture, then top with the remaining provolone slices. Add 2 more tablespoons of water, cover, and steam for another minute. Uncover and remove from heat.
Assemble the Sandwiches
Spread mayonnaise onto each hoagie roll and fill with one-third of the beef mixture.
Serve
Serve immediately while hot.