Slice the chuck roast as thinly as possible against the grain.

Heat 1 tbsp of olive oil in a large skillet over medium-high heat. Add sliced onions and green bell peppers. Sauté for 8-10 minutes until caramelized and soft. Remove from skillet and set aside.

Add remaining 1 tbsp of olive oil to the skillet. Add the shaved beef, salt, and black pepper. Cook for 3-4 minutes until browned and cooked through.

Return the onion and pepper mixture to the skillet with the beef. Stir to combine.

Divide the meat and vegetable mixture into 4 equal portions in the skillet. Top each portion with 2 slices of provolone cheese. Turn off the heat and cover the skillet for 1-2 minutes until the cheese is melted.

Toast the hoagie rolls under a broiler for 1-2 minutes. Use a spatula to transfer each cheesy beef portion onto a toasted roll. Serve hot.