Start by washing and slicing the potatoes into thick rounds. Boil them in salted water until just tender but not falling apart. Drain well and let them steam dry for a few minutes.
Place the vegetable oil in a baking tray and heat it in the oven until hot. Carefully add the potatoes and roast until they begin turning golden and slightly crisp on the edges.
In a bowl, mix lemon juice, chicken stock, oregano, garlic, semolina (if using), and black pepper. This mixture adds bright flavor and helps create a crispy finish.
Pour the lemon mixture over the partially roasted potatoes. Toss gently to coat and return to the oven. Roast until deeply golden and crisp.
Blend feta, lemon juice, olive oil, salt, and pepper until smooth and creamy. The texture should be thick but pourable. Drizzle over the hot potatoes before serving.