In a blender, combine the cucumber, jalapeño, shallot, garlic, cilantro, lime juice, Greek yogurt, sour cream, salt, pepper, coriander, and olive oil. Blend on high speed until the texture becomes smooth and creamy. Pause to scrape down the sides of the blender if needed to ensure all ingredients are well incorporated. Taste and adjust seasoning — you may want more lime juice for brightness, salt for depth, or jalapeño for heat.
Transfer the gazpacho to a container, cover, and refrigerate for at least one hour to chill thoroughly. This resting time allows the flavors to meld beautifully. It can also be prepared a day in advance for convenience.
Meanwhile, prepare your garnishes. Finely dice cucumber and shallots, slice scallions thinly, and if using, toss the shrimp with a squeeze of lime, olive oil, and a pinch of salt. Mix the sour cream with a little water to create a smooth, pourable consistency for drizzling.
When ready to serve, pour the chilled gazpacho into bowls. Using a spoon, swirl a crescent of the thinned sour cream across the surface for an elegant touch. Sprinkle with garnishes — diced avocado, cucumber, scallions, shallots, microgreens, or edible flowers — to add texture and color.
Serve immediately, cold and refreshing, as a light appetizer or a cooling summer entrée.