Using agave nectar in the glaze helps balance the heat of the Chinese mustard. You can adjust the amount of mustard to make the flavor more or less fiery.
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.
Cabbage is packed with folate, a vitamin that has been shown to decrease the risk of heart disease and certain cancers.