Preheat the oven to 200°C (400°F).
Wash and scrub the potatoes, then cut them into evenly sized chunks.
Spread the potatoes on a large baking tray. Drizzle with olive oil and season with salt, black pepper, and dried oregano. Toss until evenly coated.
Scatter the garlic cloves around the tray and place the feta block in the centre.
Roast for 40–45 minutes, turning the potatoes halfway through, until golden and crisp.
Remove the tray from the oven and gently press or break the baked feta so it lightly coats the potatoes.
Garnish with fresh basil if using and serve warm.