Heat a large, heavy-bottomed saucepan over medium heat. Add the olive oil and the onion (minced). Then add the garlic (finely chopped) and cook. Stir occasionally for about 5 minutes or until the onion is tender. Add the mixed herbs and oregano and cook, stirring often, for about 2 minutes.
Stir in the tomatoes (chopped) and season with salt. Bring to a simmer, then reduce the heat to medium low and allow to simmer, uncovered. Stir occasionally for about 50 minutes or until the tomatoes are very tender and have broken down to form a chunky sauce.
When the sauce is done, remove the pan from the heat. Puree half of the sauce in a blender. Return the puree to the sauce remaining in the pan.
In a separate pan, cook the beef mince on high heat, stirring often, for about 5 minutes then season to taste. Mix the meat together with the sauce and season the sauce to taste
In a small bowl, whisk the vinegar and olive oil together and season with salt and pepper. Lay the zucchini, eggplant (sliced lengthwise into 5mm thick slabs) and capsicum (cored, seeded and quartered) on a large-rimmed baking tray and brush both sides of the vegetables with ¼ cup of the balsamic mixture.
Transfer the vegetables to a grill on medium high heat (in batches, if necessary) and grill until just tender and slightly charred. About 3 minutes per side for the zucchini and eggplant, and about 4 minutes per side for the capsicum. Return the vegetables to the baking trays and let cool. Cut the capsicum quarters in half.
Preheat the oven to 180°C (or 160ºC for fan forced oven).
Spread 1 cup of the tomato sauce over the bottom of a baking dish. Lay 4 uncooked lasagne sheets over the sauce, breaking them to fit (don't worry if there's space between the lasagne sheets as they will expand once cooked). Lay one third of the grilled vegetables over the sheets then spoon 1½ cups of the sauce over the vegetables and sprinkle one third of the mozzarella cheese over the sauce.
Repeat layering the lasagne sheets, vegetables, sauce and mozzarella cheese one more time.
Add the remaining 4 lasagne sheets, then spread 1½ cups of the sauce on top. Add the remaining vegetables. Spoon the remaining sauce over the vegetables.
Cover the baking dish with aluminum foil. Bake for 30 minutes at 180ºC. Remove the foil and sprinkle the remaining mozzarella cheese over the lasagne. Bake uncovered for about 15 minutes or until the cheese has melted and the lasagne is golden brown on top and heated through (if you insert a knife into the centre of the lasagne for 10 seconds, it should feel hot after you pull it out). Let the lasagne stand for 5 minutes before serving.