In large bowl, whisk together olive oil, vinegar, garlic, black olives and salt and pepper. Stir in peaches or nectarines and parsley; set aside.
Sprinkle chicken generously with salt and pepper and place over coals skin side down. Grill until breasts are just opaque throughout, about 7 to 9 minutes per side. Check for doneness by cutting into one of the breasts at the thickest point. It should appear opaque all the way through with no pinkness.
Soon after you start grilling the chicken, put the sausages on the grill and cook, rolling them around occasionally until they are done. When they are both done, cut them into bite-sized pieces and add to the bowl with the vinaigrette and peaches.
Coat pepper halves and onion slices with vegetable oil and sprinkle generously with salt and pepper. Place on grill and cook until they are well-browned. Cut into bite-sized pieces and add to bowl.
Toss all ingredients together until everything is well-coated with dressing. Transfer to serving bowl, sprinkle with shaved pecorino and serve.