Preheat the oven to 200C/gas 6/fan 180C. Carefully loosen the skin over the breast of the chicken and ease a slice or two of the prosciutto and sprig of rosemary under the skin to cover each breast. Choose the fattiest parts of the prosciutto, as the idea is for it to baste the breast meat and keep it from drying out too much. Chop the remaining prosciutto and put it in the cavity of the chicken with the onion, sage and the rest of the rosemary. Use wooden cocktail sticks to close the cavity.
Choose a baking dish that will just hold the chicken comfortably, drizzle the base with 1 tbsp of the oil and put in the chicken, breast side up. Pour over the remaining oil and season thoroughly. Roast for 11⁄4 hours, basting from time to time with the white wine, until the juices from the chicken have no trace of blood in them when the thigh joint is pierced with a knife.
While the chicken is roasting, start the sauce. Tip the garlic, parsley leaves, livers and anchovies into the bowl of your food processor with the soppressa or salami, if using. Whizz until everything, including the parsley leaves, seems amalgamated.
When cooked, lift the chicken on to a carving board, cover with foil and let it rest for 15 minutes. Pour the olive oil from the juices left in the roasting pan into a small saucepan – you should have about 4-5 tbsp. Put the pan over a low heat and gradually add the liver mixture, stirring to blend with the oil. Cook, stirring continuously until the sauce changes from a raw to a cooked colour. Pour in the lemon juice, stir, then add the white wine, and when that has evaporated, add the vinegar. After 10-12 minutes cooking, taste and season with salt and freshly ground black pepper.
Return the sauce to the cleaned food processor bowl, give it all a second whiz and return to the pan. Back on the heat, continue to stir and cook the sauce, adding water, a little at a time, until you achieve a velvety texture and a thick pouring consistency. Keep the sauce warm over a pan of simmering hot water while you joint the chicken.
Discard the backbone, carve the legs into thighs and drumsticks, and cut each breast into two, so diners get a bit of each. Discard the flavourings from inside the cavity. Add half the chopped parsley and lemon zest to the sauce and pour into a serving bowl, scatter with the rest of the parsley and lemon zest and serve with the chicken.