I have a notion, but it is an educated guess, and may not be practical to use; however, I think it's also a really cool experiment and potentially an elegant solution. It's also an alternative to an extremely long (days or more) soak in flavored liquid.
From the Cooking Issues blog, we know that you can infuse flavors into alcohol or water using a nitrous oxide cream whipper. The method is that you put liquid and herbs/seeds/fruits in the whipper, pressurize it with nitrous oxide, then release the pressure suddenly. The gas pressure forces liquid and gas deep into what you're infusing and then when the pressure is released, the gas and liquid are abruptly pulled, out, bringing flavor with it. You should be able to do this in reverse, using gas pressure to force flavored liquid into a peeled, pierced, hard-boiled egg. You'll have to use a pressure cooker or cream whipper.
Prepare HEAVILY spice flavored broth, by simmering herbs and spices for several hours to overnight in water. Maybe add a little alcohol beforehand to help extract flavors. Next, prepare lightly hard boiled eggs, peel them, and pierce them with forks until the tines reach some distance into the yolk.
Place eggs and liquid in either a cream whipper or a pressure cooker. Pressurize the vessel, and swirl or shake to help mix. Then allow to sit for a minute or two, and release pressure. If flavor doesn't carry through enough, you might need to allow it to sit for a longer period.
- Try reducing your flavored liquid beforehand for a more concentrated flavor.
- Try it with increasing portions of alcohol; many flavor compounds are more soluble in water than alcohol.
- Use a warmer liquid (warmer liquids dissolve substances better)
- Allow the pressurized vessel to sit for longer periods (may cause problems if using a pressure cooker, as it might overcook)