Rinse and core tomatoes; cut in half lengthwise. Set halves, cut side up, in a 9-inch cake pan. Brush cut sides with a total of 2 teaspoons oil. Sprinkle evenly with granulated sugar and 1/4 teaspoon salt. Bake in a 400° regular or convection oven until tomatoes are browned, 35 to 45 minutes. Let cool.
In a blender, whirl tomatoes, balsamic vinegar, red wine vinegar, remaining 4 teaspoons olive oil, brown sugar, and basil until smooth. Add salt and pepper to taste.