Preheat oven to 250°F.
Pour ½ cup olive oil in a 9- by 13-inch dish or pan. Arrange tomatoes in it, cut side up. Drizzle with remaining ½ cup olive oil. Sprinkle with oregano and salt. Bake for 1 hour.
Turn tomatoes over and bake for 1 hour longer. Turn tomatoes over again and bake until dark red and very tender. The time will depending on the ripeness of the tomatoes: 15 minutes for very ripe or canned tomatoes and up to 45 minutes for less-ripe fresh tomatoes. Layer tomatoes in serving dish, sprinkling a little garlic over each layer. Pour remaining reserved oil over the tomatoes.
* The flavor of the tomatoes improves with time. I like to let them rest for at least 2 hours before eating them. Store in refrigerator and bring to room temperature before serving.