Whisk the eggs, salt, and pepper. Add the bone broth and 1 teaspoon tamari. Whisk until smooth.
In a small bowl, combine the chicken, shrimp, mushrooms, green onion, and chili with the remaining 1 teaspoon tamari. Divide this mixture among 6 small ramekins or oven-safe tea cups. Pour the custard into the ramekins, cover with foil, and place in a roasting pan. Fill the pan with enough hot water to go halfway up the sides of the ramekins. Bake for 25-30 minutes or until the custard is just set. Garnish with cilantro and serve.