For the vegetable tian: Preheat the oven to 350 degrees F. Lightly oil a 9 by 13-inch ceramic or glass baking dish. In a small bowl, combine the oil with the thyme, garlic, salt, and pepper.
Arrange half of the vegetables in rows in the dish, interspersing the different types until the bottom of the dish is covered. Drizzle with half of the oil mixture. Make a final layer of mixed vegetables, and drizzle with the remaining oil mixture. Cover the top of the vegetables with lightly oiled parchment paper. Bake until the vegetables are tender, about 40 minutes.
Remove the vegetable tian from the oven, keep warm in a warm place, and increase the oven temperature to 450 degrees F.
For the tuna: Season the tuna with the salt and pepper. Heat the oil in a large nonstick skillet over high heat. Add the tuna and cook, turning once, until seared on both sides, about 2 minutes. Uncover the tian and place the seared tuna fillets on top of the vegetables, spacing them evenly. Bake, uncovered, until the tuna is rare to medium-rare, about 5 minutes. Spoon equal amounts of the sauce in the centers of 6 warmed plates. Using a wide spatula, lift portions of the tuna and vegetables and transfer to the plates.
For the sauce: Place the tomato confit, garlic confit, water, salt and pepper in a blender and process on high speed. With the machine running, drizzle in the oil and blend until the sauce is emulsified, about 1 minute. Transfer to a medium bowl and stir in the parsley and thyme. Set aside at room temperature
Place the tomatoes in a colander and toss with the salt. Let drain at room temperature for 2 hours. Pat the tomatoes dry with paper towels. Preheat the oven to 250 degrees F. Place the tomatoes, garlic, and rosemary in a nonreactive 2-quart saucepan. Add enough oil to cover the tomatoes. Cover the saucepan and bake until the tomatoes are very tender, but not falling apart, about 3 hours. Drain, discard the garlic and rosemary, and set the tomato confit aside for the sauce. (The tomato confit can be prepared up to 3 days in advance, covered and refrigerated.)
Place the garlic cloves and 2 cups cold water in a small saucepan and bring to a boil over high heat. Drain. Repeat the procedure 2 more times. Return the drained garlic cloves to the saucepan and add the oil. Bring to a bare simmer over very low heat. Cook until the garlic is tender, about 40 minutes. Cool completely. Transfer to a 1-pint canning jar, add enough oil to cover the garlic, and seal. (The garlic confit can be prepared up to 3 weeks in advance, covered and refrigerated.)