1. Peel, seed, and cut enough ripe papaya into 1/2-inch cubes to make 1/2 cup; reserve for garnish. Cut remaining papayas into 1-inch chunks. In a blender or food processor, combine 1-inch papaya chunks, 1/2 teaspoon chili, and orange juice; purée until smooth.
2. Pour purée into a bowl; add broth, lime juice, shallots, and additional chili to taste; mix well.
3. Ladle into wide bowls. To each bowl, add equal portions shrimp, reserved ripe papaya cubes, diced green papaya, and avocado. Add salt to taste and sprinkle with cilantro.