Working over bowl, gently squeeze tomato halves to release seeds and juices. Strain juices, pressing on solids to extract as much juice as possible (about 1/2 cup). Discard seeds. Chop tomatoes. Transfer chopped tomatoes and tomato juices to large glass bowl. Add next 9 ingredients. Let stand at room temperature 1 hour.
Working in batches, puree gazpacho with 1 cup water in blender until smooth. Pour gazpacho into coarse strainer set over large bowl. Press on solids to extract as much soup as possible. Season with salt and pepper. Chill at least 2 hours and up to 1 day. Serve cold.