Soak the bread in cold water for 15 to 20 minutes, then wring out the water. Add to a blender or food processor along with the tomatoes, cucumber, bell pepper, garlic, and onion. (Depending on the size of your blender, you may need to puree the tomatoes and bread first to make room for the rest.) Blend until pureed but with some texture to it (or finer if that’s your preference).
Add the olive oil, vinegar, salt, black pepper, and cumin. Puree to combine. Taste and adjust seasoning. Refrigerate until chilled, at least 4 hours and preferably overnight.
When ready to serve, mix equal parts salt and pimentón in a small dish. If desired, rub the rims of tumblers with a lime wedge and dip them in the salt mix. Briefly puree the gazpacho, then decant it into a pitcher or juice jar and divide it among tumblers or bowls. Swirl more oil over each portion and sprinkle with the salt mix.