Prepare the Garnish: Finely dice about a quarter of the English cucumber and a quarter of each bell pepper. Combine in a small bowl, cover, and refrigerate.
Soften and Toast: Roughly chop the remaining cucumber, bell peppers, and red onion. Tear the stale bread into small pieces and place in a bowl with 2 tablespoons of water to soften. In a dry small skillet over medium-low heat, toast the slivered almonds 2–3 minutes until fragrant and lightly golden; remove.
Create the Base: In the blender, combine the roughly chopped tomatoes, red onion, and garlic. Blend on medium for 30 seconds to create a coarse, liquid base.
Build the Body: Add the remaining chopped cucumber, bell peppers, soaked bread (and any unabsorbed water), and toasted almonds. Blend on high for about 60 seconds, until very smooth.
Emulsify the Soup: With the blender running on medium, remove the lid’s center cap and slowly drizzle in the ¼ cup extra virgin olive oil to form a creamy emulsion.
Season and Finish: Add the sherry vinegar, sea salt, smoked paprika, and black pepper. Blend for 20 seconds to combine.
Chill and Meld: Transfer to a large glass pitcher or non-reactive bowl. Cover and chill for at least 4 hours, up to 24 hours.
Serve: Stir well. Ladle into chilled bowls and garnish with the reserved diced vegetables, parsley, and a light drizzle of extra virgin olive oil.