Tom Colicchio's Caramelized Tomato Tart

For the tarts: Heat the oven to 425 degrees F. In a small saucepan, combine the sugar with the water, and heat over medium heat, swirling the pan until the sugar has completely dissolved. Then let the mixture boil, swirling occasionally, until the resulting caramel is nut-brown. Remove the saucepan from the heat. Add the vinegar to the caramel, swirling the pan until thoroughly combined. Pour the caramel into four 4-ounce ramekins. Allow the caramel to cool for 1 minute or so. Then place 1 garlic clove, 3 olives, and a tomato half into each of 4 ramekins. Add salt and pepper to taste, and top with the onion confit. Cut the pastry into rounds that are slightly larger than the opening of the ramekins (these will become the tart crusts). Place the pastry rounds over the Onion Confit. Then transfer the ramekins to a baking sheet and bake until the pastry is puffed and golden, about 20 minutes. Allow the tarts to cool for 1 to 2 minutes, then carefully turn them out onto plates. Serve warm or at room temperature. For the roasted tomatoes and garlic: Heat the oven to 350 degrees F. Cut the tomatoes in half crosswise (through the equator), and then place the tomatoes, garlic, and oil in a large bowl. Season with salt and pepper, and mix gently. Line 2 large, rimmed baking sheets with parchment paper or aluminum foil. Place the tomato halves on the baking sheets, cut side down, and then pour any oil left in the bowl over them. Divide the garlic and thyme sprigs between the baking sheets, and bake for about 20 minutes, or until the tomato skins loosen. Remove and discard the tomato skins. Pour any juices that have accumulated into a bowl and reserve. Return the tomatoes and garlic to the oven and reduce the temperature to 275 degrees F. Continue roasting, periodically pouring off and reserving the juices, for 3 to 4 hours more, or until the tomatoes are slightly shrunken and appear cooked and concentrated but not yet dry. Remove the tomatoes from the oven and allow them to cool on the baking sheets. Discard the thyme, and transfer the tomatoes and garlic to separate containers. Store the tomatoes, garlic, and reserved tomato juices (also in a separate container) in the refrigerator for up to 1 week or in the freezer for up to 6 months. For the onion confit: In a large deep skillet set over medium heat, heat the oil until it slides easily across the pan. Add the onions, and season with salt and pepper. Reduce the heat to medium-low and cook, stirring occasionally, for about 30 minutes, or until the onions are very soft but not brown. Add the stock and vinegar and simmer, continuing to stir occasionally, until the pan is dry and the onions are golden, about 30 minutes more. Add the thyme leaves and anchovies, if using, and mix well. Serve warm or at room temperature. The confit should be refrigerated and will last at least a week.