Cut cooked, peeled and deveined shrimp into ½-inch pieces and add to a large bowl. Reserve 4 whole shrimp with tail on for garnish.
Add red onion, celery, cucumber and jalapeño into the bowl, along with zest and juice of 1 lime. Fold in avocado chunks and chopped cilantro.
Pour 1 can of tomatoes into a blender or small food processor with tomato paste and ¼ cup of water. Pulse just a few times to combine and create a liquid base. Keep a few chunks of tomato for texture, if you prefer.
Pour the tomato mixture into the shrimp and veggie bowl. Season with salt, cracked black pepper and hot sauce (about 2 teaspoons gives me just enough spice), and stir to combine. If your gazpacho is thick, add another ¼ cup of water to thin.
Taste, adjust seasoning and serve in cocktail glasses. Garnish each with a tail-on shrimp.