Pre-heat the oven to 200°C / 180°C fan / gas 6. Arrange the tomatoes and garlic bulbs in a large roasting tin (cut-side up). Drizzle with two tablespoons of olive oil and season liberally with salt and pepper.
Roast for about 40 minutes, checking once to make sure the garlic isn’t burning. When the tomatoes are shrivelled and starting to caramelise and the garlic is soft and golden, remove the tray from the oven.
When sufficiently cooled, squeeze the garlic out of their cloves and discard the skins.
Heat the remaining olive oil in a large thick-bottomed pot and add the onion and carrot. Stir for a minute while it sizzles, and then reduce the heat and allow the vegetables to cook gently for about another 5 minutes.
Tip the tomatoes, garlic and basil into the pot, pour in the stock and bring to the boil. Then reduce the heat and cook on low for about 20 minutes. Check to see if it needs further seasoning before blending with a hand blender until smooth (alternatively you can transfer to a food processor).
Ladle the soup into deep bowls, add a sprig of basil and a couple of croutons, and drizzle with a little fresh cream if you like.