My mother-in-law, affectionately known as Nonna C, used to make these and they were the best, especially with good bread to soak up the flavoured oil left at the end. This is not a real recipe (Italian mother-in-laws don't use recipes!) but more a method, so quantities are more "al'occhio" - or done by sight. Experiment with different thicknesses, different vinegars and different additions to get the result you really like. The process can be done in one day but I sometimes stretch it out to 3 days, depending on how much else I have going on at the same time.
Start by washing the eggplants and then slicing them into rounds, approx 2-3mm thick. Leave the skin of the eggplant on. If the eggplants are really wide, you might cut them into strips instead.
Layer them in a colander with a generous sprinkling of salt between each layer of slices. Sit the colander in a bowl as the salty water will start to drip out soon enough. Place a weight over the eggplants to help squeeze the water out. Leave this several hours or even overnight.
When you are satisfied that a lot of water has been removed, very briefly rinse the salted eggplant to get rid of any excess salt. Pat dry with a clean tea-towel.
Next, get yourself some decent vinegar. Nonna C would use the cheap stuff but I do prefer the flavour of an Italian white wine vinegar. Really, here the choice is your own but it will make a difference to the taste of the final product.
Place a wide and shallow frypan on medium heat and pour an amount of the vinegar in the pan so that you have a depth of at least 1cm of vinegar. Once it starts to bubble, add the eggplant slices in a single layer. Leave them in the vinegar for a minute or so then turn over and do the same to the other side. Remove and set these aside and repeat with the remaining eggplant slices until all have gone through the vinegar hot bath. You might need to top up with more vinegar as some of it will evaporate and/ get absorbed by the eggplant.
Once they're all done, I place them back in the colander and then place the weight over the top once again. Leave this overnight to drain off the excess vinegar. (Alternatively, you can squeeze handfuls of the slices of eggplant with your hands to speed up the process).
The final step is the sott'olio part, or the preserving in oil. You'll need some clean and sterile jars, olive oil, your choice of dried herbs (I use oregano, Nonna C used mint), chopped garlic and dried chilli flakes.
Place a thin layer of olive oil in to cover the base of the jars and add your eggplants to the jars with all of the other flavourings. As you do this, add olive oil to make sure all the layers of eggplant are coated in the oil. Once you've filled the jars, add more oil to cover the eggplants. Any bits left uncovered will quickly go mouldy. Store in a cool and dry place, but not in the fridge as the olive oil will go cloudy.
The hardest part is leaving them for about a month before you eat them, but it is recommended so as to give the vinegar a chance to mellow. Check occasionally to make sure the eggplant is still covered in oil. Buon appetito!