If you are cooking the bouyiourdi in the oven, preheat the oven to 375 F. Otherwise, preheat the barbecue to medium-high.
Cut a piece of aluminum foil, large enough to create a loose packet around the feta cheese.
On the aluminum foil, place the onion slices.
Place the feta on top of the onions, and the peppers and the tomatoes.
Sprinkle with freshly ground pepper and the oregano.
Drizzle with the olive oil.
Fold the ends of the foil to make a packet, taking care to raise the folded ends slightly to avoid the juices running out of the packets.
If cooking in the oven, place the packets in a cookie sheet and bake for about 20 minutes.
If cooking on the barbeque, place the packets the directly on grilling rack.
Remove from the oven or the barbeque, open the packets and transfer the contents to a serving place and drizzle with the juices at the bottom of the packet.
Note: the packets are extremely hot and you should be very careful when opening them as the steam escaping can burn your hands.