Heat butter and olive oil in a large skillet. Add sliced onions and cook slowly over medium heat. Stir often for about 15 minutes. The onions should become soft, golden, and sweet-smelling without burning.

Push onions to one side of the skillet. Add ground beef to the empty side. Break the meat apart using a wooden spoon. Cook until fully browned and no pink remains in the skillet.

Stir garlic, onion powder, garlic powder, thyme, salt, and black pepper into the beef mixture. Cook for about one minute. The garlic should smell rich and fragrant without turning dark or bitter.

Sprinkle flour over the meat mixture. Stir well until combined. Slowly pour in beef broth while stirring constantly. Add Worcestershire sauce and ketchup. Let everything simmer gently for five minutes until thick and glossy.

While the filling cooks, lightly toast the hamburger buns. Toasting helps the bread stay firm and prevents soggy sandwiches. Warm buns also taste better with the cheesy beef mixture.

Spoon the beef mixture onto the toasted buns. Place provolone cheese slices on top. Let the cheese melt slightly from the heat. Sprinkle fresh parsley over everything before serving warm.