1. Trim the excess fat from the hens and reserve at least 2 tablespoons of trimmings and fat. In a 4-quart saucepan or Dutch oven, add the hens, 10 cups water, salt, and 3 scallions. Bring to a simmer and reduce the heat to low so the water just barely bubbles. Simmer for 30 minutes. Remove the hens and allow to cool; strain and reserve the broth.
2. In a medium saucepan, melt the reserved fat and the sesame oil over medium heat. Remove any skin or browned bits. Add the garlic and 2 1/2 tablespoons ginger and cook until fragrant, about 1 minute. Stir in the rice and toast until opaque, about 2 minutes. Add 3 cups broth and 3 scallions, cover, and simmer, about 20 minutes.
3. Stir together the soy sauce, brown sugar, and 2 tablespoons broth until the sugar dissolves. In a separate bowl, combine the remaining 1 tablespoon ginger and 1/2 cup broth. In a third bowl, combine the Sriracha and 2 tablespoons broth.
4. Place half a hen and a small bowl of broth on a plate along with some rice, 1 green onion, and condiments on the side. Spoon the broth and condiments over the rice, or as desired.
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