Heat the olive oil in a large skillet over medium-high heat. Add the ground beef and cook, breaking it up with a wooden spoon, until browned and no longer pink, about 5 minutes. Drain off the excess fat.
Add the onion, bell pepper, mushrooms, and garlic to the skillet. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes.
In a small bowl, whisk together the Worcestershire sauce, ketchup, cornstarch, and beef broth until smooth. Pour into the skillet and stir to combine. Bring to a simmer and cook until thickened, about 2 minutes.
Season with salt and pepper. Reduce the heat to low and stir in the shredded provolone until melted.
Serve the mixture on toasted brioche buns. Enjoy immediately.
