Make the peppers. Heat the olive oil in a large skillet over medium. Add the peppers, onions, oregano, salt and pepper. Cook, stirring occasionally, until softened; 10-15 minutes. Add the garlic, Worcestershire and red wine vinegar. Stir, and cook for 3 more minutes until well combined. Taste and adjust seasoning to your liking.
Heat a cast iron skillet or griddle over medium high heat until very hot; 3-5 minutes. Brush the skillet with half of the butter and add two portions (or however many you can fit without crowding) of the beef. With two spatulas or a grill press, smash the beef down into ½ inch thick patties, season with salt, and cook for 2 minutes. Flip the patties, top one patty with American cheese and the other with provolone and cook for an additional 1-2 minutes. Repeat with the remaining butter, beef and cheese.
Lightly toast the buns on the griddle.
To assemble, stack two patties on the bun, one with provolone and one with American cheese. Top with the peppers and onions.
Enjoy!