Soak chicken livers for 20 minutes in cold water with a tablespoon of salt. Rinse and set aside. Remove any white lines that you see in the livers and discard (or give to your dog or cat). Cut livers in half and again in half, so all are the same size.
Heat 2 tablespoons of ghee/clarified butter and 1/2 tablespoon of oil in a large pan. Using a paper towel, pat liver dry. Season the livers with salt and pepper and mix together. Just before cooking, dredge lightly with flour, shaking off the excess, using a sieve. Once the butter foaming subsides, add some of the liver to the pan; do not overcrowd the pan. Cook in batches.
Cook until still lightly pink inside, as with calves liver, about 3 to 4 minutes. Shake pan as they cook. They are done when you press them with your finger and they are not soft anymore. Remove livers to plate.
In a second frying pan, melt 2 tablespoons of butter. When the foaming subsides, add mushrooms to the pan. Brown them slightly. Watch and shake the livers simultaneously as you cook the mushrooms.
Add diced ham to mushroom pan and add about 2 tablespoons chopped shallots.
Make sauce in liver pan: Add shallots, wine/vermouth to pan, add stock and thicken with the a tablespoon of cornstarch diluted in 1 tablespoon of cold wine/vermouth. Let cook, bring to the simmer and add livers and mushroom mixture. It should thicken up a little more because of the flour in chic livers. That's done: you can make this ahead then reheat when ready to serve over mashed potatoes, with cooked, buttered peas on the side.