Preheat a grill to high. Soak the minced shallot in cold water, about 10 minutes. Meanwhile, mix 1 tablespoon lime juice, 2 tablespoons olive oil, and salt and pepper to taste in a shallow dish; add the chicken and turn to coat. Grill the chicken until golden and cooked through, about 3 minutes per side. Let cool, then slice.
Crush half of the croutons; set aside. Soak the remaining croutons in 1/4 cup water, 5 minutes, then squeeze out the water and put in a blender. Drain the shallot and add to the blender along with half each of the diced tomatoes, cucumber and bell pepper. With the motor running, drizzle in the remaining 3 tablespoons plus 1 teaspoon olive oil. Add 2 cups ice and blend until smooth. Stir in half of the cilantro and the remaining lime juice; season with salt and pepper.
Divide the soup among bowls. Top with the chicken, the remaining tomatoes, cucumber, bell pepper and cilantro and the crushed croutons. Drizzle with olive oil and serve with the lime wedges.
Photograph by Antonis Achilleos
Courtesy of Food Network Magazine