Preheat the oven to 425 degrees F. Pulse the banana peppers, olives, 1/4 teaspoon oregano and 1 tablespoon olive oil in a food processor until finely chopped.
Split open the loaf of bread, leaving one side attached. Brush the inside with 2 tablespoons olive oil. Fill with a layer of tomato, then salami, ham, coppa and provolone. Top with the banana pepper mixture. Wrap the sandwich tightly in foil and press between 2 baking sheets; place a cast-iron skillet on top to weight it down. Bake until the bread is crisp and the cheese is melted, about 20 minutes.
Meanwhile, whisk the banana pepper brine, remaining 1 tablespoon olive oil, remaining 1/4 teaspoon oregano and a pinch each of salt and pepper in a large bowl. Toss with the romaine. To serve, unwrap the sandwich and cut into pieces. Serve with the salad.