Prepare the fish: rinse the Whole Red Mullet (barbounia) under cold water, remove any remaining scales and pat very dry with paper towels. If not already gutted, remove the entrails and rinse the cavity, then dry inside and out.
Make shallow diagonal scores on both sides of each fish to help them cook evenly and to prevent the skin from curling.
Season the fish: brush both sides and the cavity with Extra-virgin Olive Oil, then season generously with Sea Salt, freshly ground Black Pepper and a sprinkle of Dried Oregano (rigani). Slip a couple of thin slices of Lemon into each cavity for added aroma.
Preheat a grill or grill pan to high (you want hot, direct heat). Oil the grates or the pan lightly with more olive oil to prevent sticking.
Grill the mullet over direct heat: place the fish skin-side down and cook undisturbed for 3–4 minutes, until the skin is crisp and releases easily from the grate. Flip carefully and cook another 2–4 minutes on the other side, until the flesh is opaque and flakes easily with a fork (timing depends on size).
Transfer the fish to a platter, drizzle with a little more extra-virgin olive oil, and finish with a squeeze of Lemon Juice. Sprinkle a final pinch of oregano and sea salt to taste, then serve immediately with lemon wedges.
