Preheat a large skillet over medium-high heat. Add a tablespoon of olive oil. Once shimmering, add the diced onion and green bell pepper (and mushrooms if using). Sauté until softened and translucent, about 5-7 minutes.

Push vegetables to one side. Add ground beef to the empty side and break it up with a wooden spoon. Season with salt and pepper. Brown until no pink remains, about 5-8 minutes. Drain excess grease if needed.

Stir in minced garlic and smoked paprika. Cook for 1 minute until fragrant. Mix meat and vegetables together.

Pour in beef broth and Worcestershire sauce. Bring to a simmer.

If thicker sauce desired, mix flour with cold water to make slurry. Add to pan, stir for 2 minutes until thickened. Reduce heat to low.

Preheat broiler to low. Lay hoagie rolls open-face on baking sheet. Spoon hot meat mixture onto bottom halves.

Top with provolone slices.

Broil for 1-2 minutes until cheese is melted and bubbling. Watch closely.

Top with roll tops or serve open-face.