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Put the brie, cream cheese, gruyère, half the parmesan, the milk and cornflour into a food processor, and blitz until smooth. Stir through the thyme and a little black pepper. Spoon the chutney into an ovenproof baking dish (ours was 15cm round) and spread it over the base. Top with the cheese mixture, spread to cover the chutney, then scatter over the remaining parmesan. It can now be covered with cling film and chilled for up to 3 days.
Heat oven to 160C/140C fan/gas 3. Put the baking dish on a baking tray and cook for 25 mins until bubbling. Turn the grill to a medium-high setting and grill for 2-3 mins or until golden brown and crispy on top. Remove from the oven and leave to cool for 5 mins before serving with crusty bread for dunking.