Preheat the oven to 400°F (200°C). Oil 2 rimmed baking sheets.
Lay the tomatoes, cut side up, in a single layer on the prepared baking sheet. Brush with the ¼ cup olive oil and sprinkle with ½ teaspoon salt. Roast until the tomatoes are slightly shrunken, about 20 minutes. Reduce the heat to 225°F (110°C) and continue to roast until the tomatoes have softened, collapsed onto themselves, and are slightly caramelized, about 2 hours longer.
Remove from the oven and let cool to room temperature. Season to taste with salt, then serve.