Preparation

• Heat the oven to 350°F. Line a 12×17-inch rimmed baking sheet or two 9×12-inch rimmed baking sheets with foil. If you have parchment, put a sheet on top of the foil. Coat the pan or pans with 3 Tbs. of the olive oil.

• Cut the tomatoes in half through the equator (not through the stem). Arrange the halves, cut side up, on the baking sheet, turning to coat their bottoms with some of the oil. Sprinkle a pinch each of salt and sugar over each half, and drizzle each with a few drops of balsamic vinegar. Arrange the garlic over the halves and top with a generous sprinkling of thyme. Pour the remaining 1 cup olive oil over and around the tomato halves.
• Roast in the center of the oven until the tomatoes are concentrated, dark reddish brown (with deep browning around the edges and in places on the pan) and quite collapsed (at least half their original height; they will collapse more as they cool), about 3 hours for very ripe, fleshy tomatoes, about 4 hours for tomatoes that are less ripe or that have a high water content. Let cool for at least 10 to 15 minutes and then serve warm or at room temperature. Be sure to reserve the tomato oil (keep refrigerated for up to a week) to use on its own or in avinaigrette.
• Quicker-cooking variation:Remove the seeds and gelatinous pulp (poke them out with your fingers) before roasting. These tomatoes cook more quickly (check for doneness after 2 hours) but yield a slightly flatter, less meaty—but perfectly pleasant—result.
• Plum tomato variation:Substitute plum tomatoes, cut in half through the stem end and seeded. The roasting time will be about 2 hours. Roasted plum tomato halves hold together particularly well; layer them in a terrine or roll them up, stuffed with goat cheese and basil, as an appetizer.

Make Ahead Tips

To store the tomatoes, refrigerate for up to a week or freeze for up to a couple of months. They’ll continue to release juice during storage.