Prepare the Shells: Use an egg topper to remove the top of each egg. Transfer 3 whole eggs and 1 yolk to a mixing bowl. Store the remaining 8 whole eggs and 1 egg white in an airtight container in the refrigerator and use within 2 days. Wash the empty shells and place in boiling water for 2 minutes. Remove the inner membrane from each shell, then drain and set upright in an egg holder.
12 eggs
Make the Custard: Add the water, broth, sake, soy sauce, mirin, and shiro dashi to the bowl with the eggs and whisk until fully combined. Strain through a fine mesh strainer.
Divide the custard evenly among the 12 prepared shells. Place the shells in a steamer rack set over about 1 inch of water in a large pot. Steam on low for 13 to 15 minutes. Turn off the heat and let sit, partially covered, for 5 minutes.
Make the Shallot Chili Crisp: Combine the dehydrated shallots, scallions, ginger, toasted sesame seeds, black sesame seeds, sugar, and crushed red pepper flakes in a small heatproof bowl. Heat the avocado oil in a small saucepan over medium heat until hot but not smoking. Pour the oil immediately over the bowl, then add the rice vinegar and soy sauce and stir to combine.
Serve: Score the surface of each steamed egg with a sharp knife. Spoon the shallot chili crisp over each egg, sprinkle with chives, and place edible flowers and that is it.