Preheat grill to low to medium (about 400F). Place soaked plank on grates and close lid. As plank begins to smoke and crackle, lift lid and place 10 tomato halves and 4 garlic cloves on hot plank. Close lid. Grill tomatoes and garlic until soft, usually about 8-10 minutes. Garlic may be done sooner that tomatoes. Remove from grill and set aside to cool.
Peel tomatoes and set aside. Peel garlic and coarsely chop. In a large saucepan heat olive oil, add onion, and cook over moderate heat until soft, but not brown (about 10 minutes). Add garlic, bay leaves, horseradish, and coriander cook about one minute. Add chopped tomatoes, stock, and sugar. Cover and cook until tomatoes are soft, about 10 minutes.
Puree soup with butter and smoked tomatoes, working in batches. Strain soup into a clean saucepan. Reheat and stir in basil, salt and pepper to taste. Serve in bowls and garnish with fresh basil leaves and cheese.
