In a large bowl combine tomatoes, cucumber, orange sweet peppers, jalapeño, and garlic. In a food processor process mixture, half at a time, with several on/off turns until you have large chunks. Place all of the mixture in the food processor bowl. Add lime juice, honey, cilantro, ginger, and 1/4 teaspoon sea salt. Cover and process with several on/off turns until the mixture is just a little chunky. If desired, season to taste with additional sea salt. Can add a small amount of V-8 juice if your soup is too dry.
To serve, place 2 to 3 ice cubes in each of four shallow bowls; ladle soup over ice. Serve with lime wedges and green onions.