First make the filling. Chop the shallot and garlic. Heat the oil in a frying pan and gently sauté the onion and garlic. Meanwhile, chop the chicken liver & mushrooms into very small pieces.
When the onion is soft, add the mushroom, liver & thyme. Season with salt & pepper, then stir for a couple of minutes until the liver has changed colour. Add the wine or brandy, put a lid on and saute over a low heat for about 5-8 minutes. Take the lid off, turn the heat up and reduce the liquid almost completely. Set aside. When cooled, transfer to a bowl, add the parsley and mash with a fork (or use a food processor). You should get thick, textured paste. Set the filling aside until you’re ready to cook the chicken.
Preheat the oven to 180°C. Lightly oil a baking dish.
Put the chicken thighs on a large chopping board, then scatter some thyme leave over them and season with pepper. Put a spoonful of the liver mixture in the middle of the chicken thighs and carefully roll them up. Put them on a plate.
Wipe the chopping board, then lay a slice of Parma ham on it. Put a chicken roll (seam-side down) on one end of the ham, then carefully roll it up - you might need to patch up small tears. Repeat with the rest of ham & chicken pieces.
Put the wrapped chicken thighs in the oiled dish, seam-side facing downwards. Brush them with oil.
Bake for about 35 minutes until the ham is golden and the chicken is cooked through. You might need to cover the dish with foil after 20 minutes or so.
Serve warm.