1) Bring a large pan of water to boil. Add the onions and cook for two minutes. Drain and cool. Peel the onions and cut off the root ends.
2) Preheat the oven to 220°C.
3) Toss the onions, vinegar, 15ml oil, 1/2 teaspoon of salt and 1/4 teaspoon of pepper in a 33cm x 23cm baking dish. Roast in the oven until the onions are tender and golden, stirring occasionally, about one hour.
4) Meanwhile, whisk the 85ml oil, lemon juice, thyme, and remaining 1/2 teaspoon of salt and 1/4 teaspoon of pepper in another 33cm x 23cm by 5cm baking dish.
5) Place the tuna steaks in the marinade and turn to coat. Let stand for 5 minutes on each side.
6) Oil the griddle and prepare the barbecue for medium-high heat.
7) Griddle the steaks to desired doneness, about three minutes per side for medium. Cut the steaks in half.
8) Transfer the steaks to a platter. Spoon the onion mixture around and serve.