Cut off two slices of sourdough bread, soak them in a bowl of cold water for 10 minutes. Squeeze out the excess water.
Add tomatoes, cucumber, peppers, onion, garlic, and bread to a blender cup, starting with the tomatoes. Blend until fully combined. Slowly drizzle in the olive oil to emulsify.
Pass through a strainer into a non-reactive bowl. Chill for at least 2 hours, ideally overnight
Prepare the cherry tomatoes as directed. Quarter a cucumber lengthwise, peel into ribbons, remove seeds, and roll into curls. Brunoise remaining cucumber flesh. Prepare basil.
Preheat oven to 400ºF. Arrange Parmesan in 4 rows, 1 inch x 8 inches. Bake 5–7 minutes until golden. Cool briefly, loosen, and transfer to a rack.
Ladle chilled gazpacho into a shallow bowl.
Fan out the tomato coins. Top with three small heaps of brunoised cucumber. Arrange three cucumber ribbons beside the heaps of brunoised cucumber.Place a halved cherry tomato in the middle.
Finish with basil chiffonade and a drizzle of olive oil around the tomato and cucumber.
Place a Parmesan tuile at an angle at the far end of the bowl.