Preheat oven to 325 degrees. Mix together tomatoes adn garlic in a nonreactive 9 x 13 inch baking dish. Whisk together oil, vinegar, thyme, brown sugar, and salt in a bowl. Drizzle over tomato mixture.
Bake until tomatoes are softened and carmelized, about 1 hour. Serve warm or at room temperature. Sauce can be stored in refrigerator up to 5 days; let cool before storing.