Wash, peel and remove seeds from cucumber. Chop the peeled cucumber, bell pepper, tomato, and shallot into large chunks.
Peel and crush the garlic. Thinly slice basil and oregano, reserving some basil for garnish if desired.
In a food processor or blender, combine prepared bell pepper, cucumber, shallot, garlic, basil, and oregano ( not the tomatoes!). Process on medium speed for 1-2 minutes until a coarse paste forms.
Next, add the diced tomatoes (no need to remove the peel), red wine vinegar and fresh-squeezed lemon juice. Process on high for 3-4 minutes until mostly smooth. Depending on the size of your food processor, you may need to do this in batches.
If the peels on the tomatoes were very thick you may need to crush the mixture through a coarse strainer or food mill to remove the solids. Once completed, return it to the food processor or blender.
While running the food processor or blender on medium to low speed, slowly add the olive oil. Process for an additional minute to completely emulsify the oil.
Pour into a bowl or large container, cover and refrigerate for at least 1 hour to let flavours merge. Adjust salt.
When ready to serve, transfer the chilled gazpacho to a soup tureen or a jug. Pour the gazpacho into small bowls or serve as appetizer shooters in small, tall glasses. Drizzle each serving with olive oil.
Garnish with chiffonade of basil (stack the leaves of basil, roll them tightly, then slice perpendicular into ribbons) and add course-ground pepper, if desired.