Mix all the ingredients except the balsamic glaze together in a bowl or other container, cover, and let sit in the refrigerator overnight.
The next day, remove the thyme and blend all the ingredients in a blender until the gazpacho is smooth. You will have about 2 quarts. For a smoother texture, strain the soup to yield about 1 quart. Refrigerate the gazpacho until ready to serve.
To complete: Ladle the cold soup into bowls and squeeze dots of balsamic glaze over the top.
Heat the vinegar in a heavy saucepan over medium heat until steam rises from the liquid. Place the saucepan on a heat diffuser and let the liquid reduce very slowly (it shouldn't simmer) for 2 to 3 hours, until it has reduced and thickened to a syrupy glaze. There should be approximately 1 cup of glaze. Keep the glaze in a squeeze bottle at room temperature for garnishing: if the glaze is too thick, warm the bottle in hot water to loosen the glaze.
Recipe courtesy The French Laundry Cookbook by Thomas Keller et al (Artisan, 2000)