Immerse cabbage leaves in large saucepan of boiling water 3 minutes; drain.
Remove center vein.
Brush cabbage leaves with 2 tablespoons of the oil.
Divide oysters among cabbage leaves; lightly sprinkle with thyme, salt and pepper.
Roll up leaves, jelly-roll style, folding in sides.
Brush outer leaves with remaining 2 tablespoons oil.
Place in foil pan, seam-side down.
Place uncovered foil pan on grill not directly over coals.
Cover grill; cook over medium-hot briquets 10 to 15 minutes or until oysters are firm and edges curled.