How to Make It
Bring a large saucepan of water to a boil and fill a large bowl with ice water. Using a sharp knife, make a shallow X in the bottom of each tomato. Plunge the tomatoes into the boiling water for 10 seconds, then immediately transfer them to the ice water. Peel and core the tomatoes and halve them horizontally. Set a strainer over a medium bowl and scoop the seeds and pulp from the tomatoes into it. Press the pulp to extract as much of the juice as possible; there should be 1 cup. If not, add enough of the tomato juice to make 1 cup.
Arrange the tomatoes, cut side up, on a large plate, sprinkle with the garlic and season with salt and pepper. Drizzle with 2 tablespoons of the olive oil and let stand for 30 minutes. Add any juices that accumulate on the plate to the strained tomato juice.
Preheat a cast-iron grill pan or preheat the broiler. Brush the baguette slices on both sides with the remaining 1/4 cup of olive oil and grill until golden, about 1 minute per side. Transfer the toasts to a large plate. Add the tomatoes, cut side down, to the grill and cook just until lightly charred, about 1 minute. Return the tomatoes to the plate and flatten slightly with a spatula.
Preheat the oven to 350°. Lightly oil a shallow 8-by-11-inch baking dish and arrange half of the tomatoes on the bottom. Sprinkle the tomatoes with 2 tablespoons each of parsley and basil and season with salt and pepper. Top with half of the toasts; repeat with the remaining tomatoes, 2 tablespoons each of parsley and basil and the remaining toasts. Pour the tomato juice over the toasts. Lightly oil a sheet of parchment paper and place it directly on the toasts. Cover the bread pudding with foil, pressing slightly to compact it.
Bake the bread pudding in the center of the oven for about 45 minutes, or until the liquid is absorbed and the tomatoes are very soft. Remove the foil and parchment and bake about 10 minutes longer, or until crisp. Let the tomato bread pudding stand for 15 minutes, then sprinkle with the remaining 1 tablespoon each of parsley and basil and serve.
The tomato juice is used if the yield of tomato pulp is less than 1 cup.