For the soup, melt the butter in a large, heavy-based pan over a low-medium heat. Add the onion and fry gently until softened, but not coloured. Season with a pinch of salt.
Add the chillies and garlic and continue to fry for a further 2-3 minutes.
Add the sugar and vinegar to the pan and bring to the boil. Continue to boil until the mixture has reduced in volume by about a quarter and thickened slightly.
Add the tomatoes to the pan and bring back to the boil. Reduce the heat until the mixture is simmering, then continue to simmer, covered, until the tomatoes have completely broken down (about 15-20 minutes).
Add the bread, basil and cayenne pepper and bring the mixture back to the boil. Remove the pan from the heat and set aside for about 15 minutes, or until the bread has soaked up some of the soup.
Blend the soup until smooth, then strain through a fine sieve and set the sieved liquid aside until needed. (The soup can be chilled in the fridge if desired, or kept warm until ready to serve.)
For the pesto, blend the basil, garlic, pine nuts and parmesan to a paste using a food processor. Season, to taste, with salt and freshly ground black pepper. Gradually add the olive oil in a thin stream, blending as you go, until all the oil is incorporated into the pesto.
For the basil oil, prepare a bowl of iced water.
Blanch the basil leaves for 10 seconds in a pan of salted boiling water, then drain well and plunge the leaves into the iced water. Remove from the bowl using a slotted spoon and pat dry with kitchen paper.
Blend the blanched basil leaves with the olive oil in a blender until smooth. Season, to taste, with salt.
Strain the basil oil through a clean muslin cloth, collect the strained liquid and chill in the fridge until needed.
To serve, pour the soup into bowls, place a spoonful of pesto on top of each, then drizzle over the basil oil. Garnish each bowl with a few extra basil leaves.