1) In a small bowl, whisk together the vinegar, 3/4 tsp salt, garlic, rosemary, and pepper. Gradually whisk in 8 tbsp of the oil to make a dressing. Set aside.
2) Preheat a stove top griddle pan or outdoor griddle to medium heat. Brush the peppers, courgettes, aubergine, mushrooms, and onion with the remaining oil. Cook the peppers until lightly browned and tender, about 5 mins per side. Transfer the peppers to a pan or large platter. Cook the courgettes, until softened and lightly browned and tender, about 3 mins per side; transfer to the pan with the peppers. Cook the mushrooms, until soft but not flabby, about 2 mins per side; set aside with the other vegetables. Cook the onions until soft, about 5 mins per side; set aside with the other vegetables. Drizzle 1 tbsp of the dressing over the vegetables and season with salt and pepper to taste.
3) To make the Dagwood sandwich: Split the bread in half to make two evenly thick square pieces. Brush the dressing on the cut sides. Make a layer of each of the griddled vegetables that evenly covers one piece of the bread, overlapping the pieces slightly, if necessary. Top with a layer of the tomatoes, season with salt and pepper. Lay the rocket on top and drizzle them with about 1 tbsp of the dressing. Finish the sandwich off with the cheese and lay the other piece of bread on top. Wrap the sandwich tightly in clingfilm. Place the wrapped sandwich on a cutting board or baking sheet and weigh it down with a heavy object, such as a cast-iron skillet, for about 1 hr. When ready to serve cut into 4 to 6 pieces equal pieces.
* Cook's Note: This is a great way to use up a variety of leftover griddled vegetables. In keeping with a true Dagwood style, feel free to improvise with the selection of vegetables and cheese.