Add the ground beef to a hot medium to large-sized skillet over medium heat. Let the meat cook for a minute or two, developing a nice sear. Flip the chunk of meat, repeating to sear the other side. Once both sides are seared use a spatula to break the meat up as much as possible. Drain the meat and return to the skillet.
Add in the salt, pepper, and Worcestershire, stirring occasionally and cooking until fully browned. Remove the meat from the pan, and set it aside.
Add the 2 tablespoons of butter to the same pan and melt. Add in the pepper and onion and cook, stirring occasionally, until the onions have caramelized. Remove the pan from heat, stir in the cooked ground beef until everything's evenly incorporated, and set the mixture aside.
Butter the outsides of all the slices of bread.
Flip four slices of buttered bread over onto a clean work space. Add a slice of cheese to the un-buttered side. Top that with a quarter of the meat mixture. Top the meat mixture with another slice of provolone. Finish it off with the un-buttered side of one of the other pieces of bread. Press the top slice of bread down gently to 'seal'. Repeat until all four sandwiches are assembled.
Heat a clean skillet or griddle to medium heat. Add one sandwich to the pan and cook until browned and the cheese on that side has melted, about 3-4 minutes. Use two spatulas to 'hold' the sandwich, and flip it cooking the other side until browned as well.
Repeat until all the sandwiches are done.