In a large bowl combine tomatoes, cucumbers, sweet peppers, chile pepper, and garlic. Place half the tomato mixture in a food processor; process with several on/off turns to large chunks. Repeat with remaining tomato mixture. Return all of the mixture to the food processor. Add lime juice, honey, cilantro, ginger, and ¼ 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.
To serve, place 2-3 ice cubes in each of 4 shallow bowls or glasses; ladle soup over ice. If desired, serve with lime wedges and scallions.