Heat olive oil in a large skillet over medium heat.
Add the sliced onion and green bell pepper to the skillet and sauté for 5-6 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Push the vegetables to the side of the skillet and add the ground beef.
Cook the ground beef, breaking it apart with a spatula, until browned and cooked through, about 6-7 minutes.
Season the mixture with salt, black pepper, and dried oregano. Stir to combine with the vegetables.
Reduce the heat to low and evenly distribute the beef and vegetable mixture in the skillet.
Place one slice of provolone cheese over each quarter of the mixture and cover the skillet with a lid to melt the cheese, about 2-3 minutes.
While the cheese melts, slice the hoagie rolls lengthwise without cutting all the way through and toast them lightly in a separate pan with butter until golden brown.
Scoop the cheesy ground beef mixture into each toasted hoagie roll.
Serve immediately and enjoy your Ground Beef Philly Cheese Steak sandwiches.