How to Make It
Scatter the wood chips in a medium cast-iron skillet and cover the skillet tightly. Heat the chips over moderately high heat until smoking. Place the 4 tomato halves on a rack and set the rack in the skillet. Cover and smoke the tomatoes for 2 to 3 minutes, or until barely softened. Transfer the tomatoes to a plate and let cool slightly, then peel them.
In a large saucepan, heat the olive oil until shimmering. Add the onion and leek and cook over moderate heat, stirring frequently, until softened but not browned, about 10 minutes. Add the coriander seeds, garlic, bay leaves and horseradish and cook until fragrant, about 2 minutes. Add the chopped tomatoes, chicken stock and sugar, cover and cook over moderate heat until the tomatoes are softened, about 10 minutes. Discard the bay leaves.
Working in batches, puree the soup with the butter and smoked tomatoes until smooth. Strain the soup into a clean saucepan; season with salt and pepper. Serve the soup in bowls, garnished with basil.