Heat the oven to 350 degrees. Arrange the tomatoes on a cooling rack over a baking sheet and season with oregano, salt and pepper. Drizzle with EVOO and roast for about 40 minutes to tart them up.
In a medium skillet, brown the pancetta (or speck or bacon) in a bit of EVOO and let cool. Place the beef and pancetta in a bowl, then add the garlic, parsley, a little salt and lots of pepper. Grind the salami and ham in the food processor into fine bits; add to the meat.
Form the meats into 4 patties, thinner at the center than at the edges for even cooking. Drizzle the meat with EVOO and cook in a hot cast-iron skillet or a large nonstick skillet over medium-high heat for 8 minutes for medium, flipping occasionally. Top with the cheese and melt. Serve on the rolls, topped with the oven-roasted tomatoes, arugula, basil, red onion and a drizzle of EVOO.