With a sharp knife, carefully remove a 1-inch core from the center of each onion. Cut each onion into four wedges to within 1/2-inch of the root end.
Place each onion on a double thickness of heavy-duty foil (about 12-inch square). Place bouillon in the centers of onions; top butter, thyme, salt and pepper. Drizzle with wine or broth if desired. Fold foil around onions and seal tightly.
Prepare grill for indirect heat. Grill onions, covered, over indirect medium heat for 35-40 minutes or until tender. Open foil carefully to allow steam to escape.
Cook's Note: These can be prepared year 'round on a grill in the summer or in an oven preheated to 350 degrees for the same amount of time in winter.