Preheat oven to 400 degrees F. Line an extra-large, rimmed baking sheet with parchment paper.
Spread corn, bell pepper, onion, garlic and shishito peppers on baking sheet. Drizzle about 3 tablespoons of olive oil over the vegetables. Season with freshly ground pepper, to taste. Sprinkle salt over everything except the corn. Salting the corn now will toughen its skin!
Roast vegetables 20 minutes, stirring halfway through cooking time. Remove from oven. When cool enough to handle, peel garlic, and remove the charred skin and seeds from the shishito peppers.
Place half of the roasted vegetables and half of the chopped tomatoes and cucumbers in a high-powered blender. Add 1 ½ tablespoons of olive oil and sherry vinegar. Squeeze in the juice of one lime. Puree until smooth, about 45 seconds. Transfer mixture to a large bowl.
Repeat blending with remaining roasted vegetables, chopped tomatoes, cucumbers, olive oil, sherry vinegar, and lime juice. Puree until smooth.
Pour into large bowl with the first batch of gazpacho. Whisk in 1-2 teaspoons of hot pepper sauce or sriracha sauce, if desired. Season to taste with salt and pepper.
Cover gazpacho and chill at least 2 hours or overnight.
Serve chilled or at room temperature, and garnish with fresh basil, lime wedges, sliced shishito peppers, and extra hot sauce as desired. Enjoy!
Notes
*Shishito peppers are small, adorably wrinkled and mild peppers compared to jalapenos.