Make the sauce: in a medium saucepan combine the sauce ingredients with 2 tablespoons water; bring to a simmer over medium heat; cook for about 1 minute, stirring occasionally; set aside half of the sauce for dipping.
Make the rub: in a small bowl, mix the rub ingredients very well, use your fingertips (works better).
Let the roast stand at room temperature 20-30 minutes before grilling.
Lightly coat the meat with the oil and season with the rub, pressing spices into the meat.
Grill over Direct Medium heat until well marked on both sides, about 10 minutes, turning once.
Move the roast over Indirect Medium heat and cook to desired doneness, 20-30 minutes more for medium-rare, brushing the meat with the remaining half of the sauce on both sides and turning it over every 5 minutes or so.