Warm oil in a saucepan over medium heat. Add onion and garlic; saute until soft and translucent ( about 5 minutes ). Mix in remaining sauce ingredients and 3/4 cup water.
Reduce heat to low; cook for about 30 minutes, stirring frequently, until you're satisfied with the taste and the sauce heavily coats the spoon. (If thats too thick for you, add more water.) Set aside.( you can also make ahead of time and store up to 2 weeks).
Prepare chicken. Rub with salt and a spritz of oil. Cover; let sit at room temperature for 20 minutes.
Heat grill to medium (when you can hold your hand 2 inches above it for 4 to 5 seconds, no more, no less.) Grill one side of the chicken uncovered for about 3 minutes; repeat on the other side.
Flip back to original side, then rotate 90 degrees, to get crisscross mark. Cook 3 minutes more, and brush on some sauce. Repeat on other side. Chicken is ready when white throughout but juicy, and sauce is a bit chewy and caramelized in spots. (for a slightly crusty surface, leave them on for an extra minute).
Serve whole, or sliced thickly, with leftover sauce.