Preheat oven to 400°F.
In a mixing bowl, combine: cherry tomatoes, thinly sliced onion, Kalamata olives, parsley, oregano, salt and black pepper and extra virgin olive oil
Toss well to combine and let sit for 2–3 minutes.
Fold each sheet of parchment paper in half, then reopen flat. On one side of each parchment sheet spoon a small layer of the tomato mixture onto the parchment
Place each red snapper fillet over the tomato mixture. Season lightly with salt and pepper.
Divide the remaining tomato mixture over the fish.
Top each packet with a little fresh lemon zest and another light drizzle of extra virgin olive oil.
Fold the parchment over the fish to form a half-moon shape. Starting at one edge, tightly crimp and fold the parchment to completely seal the packet. The tighter the seal, the better the steam environment.
Place the packets on a baking sheet and bake for 12–15 minutes, depending on the thickness of the fish. The parchment should slightly puff as the fish steams inside.
Carefully open the parchment packets (watch for steam). Finish with fresh parsley