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Heat oven to 180C/160C fan/gas 4. Melt half the butter in a large saucepan, add the onion and cook until soft. Pour in the cream and milk, and add lots of seasoning. Add the sliced vegetables and gently simmer for 10 mins until the potatoes start to soften.
Meanwhile, blend the herbs, garlic, most of the Parmesan and some seasoning in a food processor. Add the oil and blend again to form a paste.
Tip a third of the creamy veg into a buttered baking dish, dollop over half the herb mix and spread out a little. Top with another third of the veg, followed by the remaining herb mix, then the rest of the vegetables. Dot the surface with the remaining butter and scatter over the reserved Parmesan. Bake for 1-1½ hrs until bubbling and golden, covering with foil for the final 30 mins if it’s becoming too brown. Leave to rest for 10-15 mins before serving.