Tear off pieces of aluminium foil large enough to wrap the vegetables.
In a small bowl, mix together the olive oil, balsamic vinegar, thyme, oregano, salt and pepper to make a dressing. Pour the dressing over the vegetables. Mix well.
Evenly divide the vegetables and dressing between the pieces of aluminium foil. Fold the packets tightly to ensure that no steam can escape.
Place the packets on the preheated barbecue and cook for about 20 minutes, or until the vegetables are tender.
Remove the packets from the barbecue and leave to cool slightly before opening. Crumble the feta cheese over the vegetables once opened.
Serve the grilled vegetable packts immediately as a side dish at your barbecue. Enjoy!