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Heat oven to 190C/170C fan/gas 5. Cook the potatoes in boiling salted water for 6 mins, then drain well.
Mix the garlic with the oil and some seasoning. Strip the herb leaves from their stalks, then add to the oil. Drizzle a little of the oil over the base and sides of a 1.5-litre ovenproof dish. Layer half the potatoes, tomatoes and courgettes in the dish, drizzling with garlic and herb oil as you go. Mix the two cheeses and sprinkle half over the veg.
Repeat the layers of veg and oil, drizzle over the remaining oil, then sprinkle with the rest of the cheese. Bake for 40-45 mins until the veg is tender and the top golden and crisp.