Preheat the oven to 170°C.
Wrap the garlic bulb in foil and roast for 45 minutes until soft.
Squeeze out the cooled roasted garlic and chop it finely.
Whisk the cream in a mixer for 5 minutes until it separates into butter and buttermilk.
Strain the mixture through muslin, squeezing out all liquid to leave solid butter.
Mix the butter with the chopped garlic, salt, and a third of the basil.
Heat most of the olive oil in a pan and fry the shallot briefly.
Add tomatoes and remaining basil, then simmer for 3 minutes.
Char the bread in a hot griddle pan, spread with garlic butter, and warm in the oven.
Blend the soup into a fine purée and season with salt and pepper.
Drizzle the soup with olive oil and serve alongside the garlic bread.