Preheat grill to 400°F/200°C.
Place the potatoes in a large pot filled with salted water. Bring to the boil and cook, covered, for 20-25 minutes until tender but al dente. Drain well.
Lightly oil a baking tray or, alternatively, line it with baking paper.
Place the drained potatoes on the baking tray and flatten them gently using a potato masher, a large wooden spoon or other suitable tool, being careful not to crush them completely.
In a bowl, combine the melted butter or olive oil, lemon juice, crushed garlic, half the oregano, salt and pepper. Beat until creamy.
Pour the lemon-garlic mixture over each potato. Sprinkle with the remaining oregano and, if desired, drizzle with a little more olive oil. If desired, sprinkle chopped walnuts or semolina over the potatoes for extra crunch.
Place under the broiler about 8 inches from the heat source, until golden and crisp, about 15 to 20 minutes.