Heat 1 tablespoon of the oil in a nonstick skillet.
Add the onion and garlic and cook very gently, stirring frequently, until soft but only lightly colored- Remove from heat.
Coarsely grate the potatoes into a bowl and mix in the corn, oregano, beaten egg, and salt and pepper to taste- Add the cooked onion.
Heat the remaining oil in the skillet.
Divide the potato mixture in half and add to the pan to make 2 oval-shaped cakes, leveling and shaping the cakes with a spatula.
Cook the fritters over low heat for about 10 minutes, until golden brown underneath and almost cooked through, keeping them tidily in shape with the spatula and loosening them so that they do not stick to the bottom of the pan.
Sprinkle each potato fritter with the grated cheese and place under a preheated moderately-hot broiler, until golden brown.
Meanwhile, poach 1 or 2 eggs for each person, until just cooked.
Transfer the fritters to warmed plates and top with the eggs and sliced tomatoes.