Take each washed eggplant and cut off the cap. Carefully slice down the middle, leaving the stem end intact. Slice again on either side of the original slice, if it is big enough, as many times as needed for even slices, so that the eggplant can be opened into a fan shape.
Place in pan with broth. Bring to a gentle simmer, and stir occasionally, to turn the eggplant so that all sides are in the broth at some point.
Simmer 10 minutes until cooked to taste.
Remove eggplant, and, if desired. let the broth boil a moment to thicken it for use as a sauce.