Combine tomatoes, 1 tablespoon oil, and vinegar; toss gently. Place tomatoes, cut sides up, on rack. Sprinkle with salt and pepper.
Bake at 200° for 6 hours or until tender and slightly syrupy (do not overbake or tomatoes will be tough and chewy). Remove from oven; cool completely. Place 1/2 teaspoon cheese onto each tomato half. Fold slightly; secure each tomato half with 1 rosemary sprig. Place on a serving platter; drizzle with the remaining 1 tablespoon oil.
Homegrown Pure and Simple: Great Healthy Food from Garden to Table