Heat grill to high. Mix together mustard, agave nectar, 1 teaspoon oil, the garlic, and basil. Cut cabbage lengthwise into quarters, leaving core intact. Brush cabbage and scallions with remaining 2 teaspoons oil.
Grill cabbage, flat side down, 3 minutes. Flip, and continue to grill until charred. Remove from grill. Add scallions to grill, and cook until partially charred, flipping halfway through cooking, about 2 minutes total.
Brush cabbage and scallions on all sides with mustard glaze. Cut scallions lengthwise into thirds. Arrange cabbage on a platter, and top with scallions.