How to Make It
To prepare hot sauce, process all sauce ingredients in a blender until smooth.
To prepare chicken, coarsely chop 2 ounces fresh ginger; mince remaining 1 ounce ginger. Bring 12 cups water, chopped ginger, cilantro sprigs, garlic head, and 2 teaspoons salt to a boil in a large Dutch oven over high. Add chicken. Reduce heat to medium and cover. Simmer 20 minutes. Remove from heat. Let chicken stand in broth until cooked through, about 30 minutes. Remove skin. Pick meat from chicken and reserve; discard skin and bones. Pour broth through a fine wire-mesh strainer into a bowl; discard solids. Reserve 4 cups broth; reserve remaining broth for another use.
Place oil, minced garlic, and minced ginger in a large saucepan; cook over high, stirring often, until garlic sizzles and ginger turns golden, about 30 seconds. Add rice, 3 cups reserved broth, and remaining 1/2 teaspoon salt; bring to a boil. Cover and simmer 12 minutes. Remove from heat. Let stand 12 minutes; fluff with a fork.
Spread rice on a platter. Top with chicken; pour remaining 1 cup reserved broth over chicken. Arrange tomato wedges and cucumber slices on rice. Sprinkle with scallions and cilantro. Serve with hot sauce and sweet soy sauce.