Blend tomatoes, green pepper, onion, cucumber, garlic, and basil in a food processor until smooth.
Pass the mixture through a fine sieve into a bowl and discard the remaining pulp and skin.
Return the sieved liquid to the cleaned food processor and blend while slowly adding extra virgin olive oil and sherry vinegar.
Season the soup with salt and pepper to taste, then chill in a covered container in the fridge.
Preheat the grill to high and place baguette slices on a baking tray.
Drizzle bread with olive oil, season with paprika and salt, and toast for 1-2 minutes per side until golden.
Ladle the cold soup into bowls containing ice cubes and top with baguette slices, chopped onions, peppers, and basil.