Preheat oven to 250 degrees. Pour 1/2 cup oil into 13 by 9 inch glass or ceramic baking dish. Arrange tomatoes in dish, cut side up. Drizzle with remaining 1/2 cup oil. Sprinkle with oregano, sugar and salt. Bake 1 hour. Using tongs, turn tomatoes over. Bake 1 hour longer. Turn tomatoes over again. Bake until deep red and very tender, transferring tomatoes to plate when soft (time will vary, depending on the ripeness of the tomatoes), about 15-45 minutes longer.
Layer tomatoes in medium bowl, sprinkling garlic and parsley over each layer, reserve oil in baking dish. Drizzle tomatoes with reserved oil, adding more if necessary to cover. Let stand at room temperature 2 hours. (To do ahead: cover, chill up to five days. Bring to room temperature before serving.)
Serve with aged goat cheese and toasted baguette slices.