For the soup, place all of the vegetables, garlic and basil for into a food processor and blend until smooth. Pass the mixture through a fine sieve to remove most of the pulp and skin, which you should then discard.
Lightly rinse the bowl of the food processor to remove any pulp and skin, then pour the sieved soup back into the food processor. Blend again, while slowly pouring in the extra virgin olive oil through the feeder, followed by the sherry vinegar, until well combined. Season, to taste, with salt and freshly ground black pepper.
Transfer the soup to a container and chill, covered, in the fridge until ready to serve.
For the garnish, preheat the grill to high.
Place the slices of baguette onto a baking tray and drizzle with olive oil. Season the baguette slices with paprika and salt, then toast under the grill for 1-2 minutes on both sides, or until golden-brown all over.
To serve, place an ice cube into each serving bowl and ladle over the soup. Float the crisp baguette slices over the soup, scatter over the finely chopped spring onions and peppers and garnish with a few basil leaves.