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Half-fill a large bowl with water and add the lemon juice. Peel the artichokes, then toss the peelings with the vegetable oil in a bowl and set aside. Chop the artichokes into rough chunks and submerge them in the lemony water.
Melt the butter in a large saucepan, and add the onion, potato, and seasoning. Drain the artichokes and stir them in. Cover the pan and sweat gently for 15 mins, stirring now and again.
Pour in the stock, cover and simmer for 10-15 mins until the vegetables are completely tender. Whizz the soup in a blender or with a stick blender until very smooth, return to the pan, then add the cream and season to taste.
Meanwhile, prepare the skins. Heat oven to 220C/200C fan/gas 7 and line a baking sheet with baking parchment (not foil, they will stick). Scatter the skins over, and roast for 10 mins. Turn them over, scatter with the Parmesan and rosemary and roast for 5 mins more or until crisp and dry, then season with a pinch of flaky salt and pepper. Serve the soup in bowls, add a swirl more cream (if you like) and top with the crisp skins.
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