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Fill a large pan with boiling water from the kettle and set over a medium-high heat. Cook the whole, unpeeled sweet potatoes for 30 mins until very tender when pierced with the tip of a sharp knife. Drain well and leave to cool for 10 mins, then peel.
Heat the oven to 180C/160C fan/gas 4. Unravel the shortcrust pastry and use it to line a 23cm fluted tart tin. Line with baking parchment and fill with baking beans, then bake for 20 mins. Remove the parchment and beans and bake for another 5 mins.
Tip the peeled sweet potatoes into a large bowl with the butter and mash with a potato masher until completely smooth. Tip in the sugar, milk, eggs, spices and vanilla and whisk until everything is combined and smooth.
Tip the sweet potato filling into the pastry case, smoothing the top with a spatula. Bake for 50-55 mins until the pastry and the surface of the pie is golden and the middle is set. Leave to cool completely in the tin, then remove to a cake stand or serving plate and cut into slices to serve.