Chop the garlic, rosemary, pepper and sea salt together and mix with virgin olive oil. Rub the outside of the chicken all over with the rosemary mixture. Place the Prosciutto and Parmesan rinds inside the cavity and allow to sit refrigerated overnight.
Preheat oven to 375 F and preheat grill.
Place onion disks and giblets in bottom of a small heavy bottomed roasting pan. Place chicken on top of onions, breast side up. Pour glass of Lambrusco over onions and rub chicken all over with 4 tablespoons balsamic vinegar. Place in oven and cook for 1 hour and 10 minutes, or until a skewer pushed into thickest part of the thigh shows clear -- not bloody -- juices.
Cut the Radicchio in half lengthwise and place it on the grill and cook for 3 to 4 minutes per side. Remove from grill and brush with extra virgin olive oil and set aside. Remove bird from oven and allow to rest 5 minutes. Transfer the chicken to a carving platter. Put onions and giblets in a bowl, with the juices. Carve the chicken, drizzle with remaining vinegar and serve immediately.