Some Greek seafood dishes remind me of southern Italian cooking, but I've never tasted one quite like this in Italy.
Combine 1½ teaspoons salt, ¼ teaspoon pepper and the oregano in a small dish. Rub over surface of fish. Let stand at room temperature for an hour.
In a blender or mini-blender container, combine 1/3 cup olive oil with the lemon juice, mustard, zest and garlic. Blend until smooth and emulsified. Season with salt and pepper (lightly, because the fish has been seasoned), and blend briefly.
Set oven on broil or prepare a hot fire on grill. Place fish skin side down on a well-oiled grill pan in top third of oven or directly on a clean, oiled grill grate. Broil or grill until just cooked through, 8 to 10 minutes.
* Alternatively, choose other fish that stand up to the heat of an oven or grill, such as snapper or grouper. More strongly flavored fish such as mullet or bluefish would be good choices as long as they are extremely fresh.