In a large pot of salted, boiling water, cook rice until tender. Drain, set aside, and keep warm.
In a food processor or blender, combine shallots, garlic, chopped cilantro, ginger, tamarind paste, anchovy, and brown sugar and puree until smooth.
In a soup pot, combine puree, cayenne, fish sauce, and clam juice and bring to a boil. Add fish and let simmer for 5 minutes. Add rice and simmer for 2 minutes. Remove soup from the heat and stir in lettuce, radishes, and snow peas. Ladle soup into bowls and serve sprinkled with scallions, cilantro leaves, and cucumber.