Cut three-quarters of the cucumber into 1-inch pieces and purée in a blender with the red peppers, tomato juice, toasted bread, 6 Tbs. olive oil, 2 Tbs. vinegar, garlic, cumin, and 1/2 tsp. each salt and pepper (you may have to purée the soup in batches, depending on the size of your blender). Taste and season with more salt and pepper if needed, and refrigerate until cold, at least 30 minutes and up to 1 day.
Heat 1 Tbs. of the olive oil in a large (12-inch) skillet over high heat until it’s shimmering. Add the shrimp and cook, tossing, until it starts to brown and lose its raw color, about 2 minutes. Stir in the thyme, 1/2 tsp. pepper, and 1/4 tsp. salt, and cook until the shrimp are just cooked through, about 1 minute. Transfer to a plate to cool.
Just before serving, cut the remainder of the cucumber into 1/4-inch dice (about 1/2 cup) and toss with the remaining tablespoon extra-virgin olive oil, the remaining 1 tsp. sherry vinegar, and 1/2 tsp. salt. Serve the soup cold in individual bowls, garnished with the cucumber and shrimp.