||Preheat grill to high.
||In medium bowl, stir together brown sugar, garlic powder, onion powder and salt. Rub mixture all over split breast pieces, being sure to get under the skin; discard any unused rub.
||Place breasts on grill and cook over medium-high, indirect heat.
||While breasts are cooking, drizzle about 1 tablespoon of oil on onions. Grill over direct heat about 5 minutes, or until lightly browned.
||In food processor, combine vinegar, mustard and peppercorns; pulse until beginning to blend. Slowly add remaining oil, pulsing to incorporate. Add grilled onions and pulse until mixture is well blended.
||Remove breast from grill when a meat thermometer inserted into the thickest part of the breast reaches 170°F, 45 to 55 minutes.
||Serve with Green Onion Sauce.