1/4 cup olive oil, plus more for brushing on vegetables
1 1/2 pounds vine tomatoes, halved crosswise (about 3 medium tomatoes)
1 yellow bell pepper, stemmed, seeds and membranes removed, and quartered
1 tablspoon thinly sliced mint leaves, divided
1 red bell pepper, stemmed, seeds and membranes removed, and quartered
Hot sauce, such as Tabasco
2 ears corn, shucked
1/2 English cucumber, peeled, seeded and diced (about 1 cup)
1/4 medium red onion, stem end left intact
1 cup tomato juice, chilled
Coarse salt and ground pepper
Heat a charcoal or gas grill to medium-high. Brush peppers, corn and onion with olive oil; season with salt and pepper.
Place on grill and cook briefly, just enough to char the vegetables slightly, about 2 1/2 minutes per side for the peppers and onion and 3 1/2 minutes for the corn. Remove from grill.
Brush cut side of tomatoes with olive oil and season with salt and pepper. Place on grill, cut side down, and cook until lightly charred, 2 to 3 minutes. Remove from grill and allow to cool.
Coarsely chop peppers, onion and tomato (discard stem and core) and cut kernels from corncobs.
Place peppers, onion, tomato and half the corn in a food processor or blender. Add 1/2 teaspoon salt, vinegar, 1/4 cup olive oil, half the mint, and several dashes of hot sauce; process until mixture is well blended.
Transfer mixture to a nonreactive container and chill.
In a small bowl, combine cucumber with remaining corn and mint; chill.
Stir tomato juice into the pureed vegetable mixture. (Note: The consistency of your soup will depend greatly on the produce used. If it seems too thick after blending, add more tomato juice. If it seems thin, use less.)
Divide soup among four bowls and top with the cucumber-corn mixture. Serve cold.