Optional Brining Step: wash & pat the roast dry with paper towels. Do not trim the thin layer of fat on the outside of the roast. Rub the roast all over with the sugar and salt. Place in a zip lock bag and refrigerate overnight. When ready to cook, remove the roast from the bag, rinse well and pat dry.
Tie the roast in several places with kitchen twine (helps the roast to cook evenly). Rub the roast all over with the garlic, pepper, soy sauce, brown sugar and thyme. Let sit until roast comes to room temperature, about 30 minutes.
Preheat grill. Place the roast on one side away from direct heat and grill, turning occasionally with tong to cook evenly for about 35-45 minutes (depending on thickness of the roast, until the internal temperature reaches 145-150 degrees.
Remove from the grill and let rest for 10-15 minutes before slicing. Remove the kitchen string and slice as desired.