Step 1 Heat the oven to 300 degrees. Place the tomatoes on a baking sheet and sprinkle half the garlic, plus the thyme, sugar, one-fourth teaspoon salt and one-eighth teaspoon pepper. Bake until the tomatoes are shriveled, 3 to 3 1/2 hours. Cool to room temperature.
Step 2 Coarsely chop the tomatoes. In a medium skillet, heat the olive oil over medium heat and cook the remaining garlic until it softens, about 2 minutes. Stir in the tomatoes and the tarragon and cook for 2 minutes. Season with salt and pepper to taste.