Preheat grill to medium.
Place garlic cloves on a small piece of foil. Place on the grill along with the lemon halves (cut-side down). Grill until the lemon has distinct grill marks and the garlic has softened, 4 to 6 minutes.
When cool enough to handle, juice the lemon. Remove and discard the garlic skins and finely chop the garlic. Place the lemon juice and the chopped garlic in a jar with a tight-fitting lid. Add oil, basil, maple syrup, pepper and salt. Cover and shake well to combine.
