Prepare a large bowl of cold water and squeeze in the juice of half a lemon.
Peel the knobbly Jerusalem artichokes and drop them straight into the lemon water to prevent them from discolouring.
In a large saucepan, heat a splash of sunflower oil over a medium heat.
Add the chopped onion, garlic, and grated potato.
Fry until golden, scraping the bottom of the pan to lift any stuck bits – this adds colour and flavour.
Transfer the cooked onion mixture to a separate bowl.
Add a little more oil to the pan.
Drain the artichokes well and add them to the hot pan, stirring over a high heat until they are golden on all sides.
Return the onion mixture to the pan with the artichokes.
Pour in the white wine, add the sprig of thyme, and top up with enough cold water to just cover the vegetables.
Bring to a simmer and cook gently for 10–15 minutes, until the artichokes are tender when pierced with a knife.
Preheat your oven to 180°C (350°F) / 160°C Fan / Gas Mark 4.
Remove the thyme sprig and discard it.
Using a slotted spoon, lift the vegetables out of the pan and divide them between four individual ovenproof pie dishes or one large pie dish.
Increase the heat under the saucepan to bring the remaining liquid to a boil.
Let it bubble away and reduce by about half. This will concentrate the flavours beautifully.
While the sauce reduces, roll out your puff pastry on a lightly floured surface.
Cut out lids slightly larger than your pie dishes to allow for shrinkage during baking.
Once the sauce has reduced, lower the heat.
In a small bowl, mix the cornflour with a splash of cold water to form a smooth paste.
Whisk this paste into the sauce; it will thicken very quickly.
Season with salt and pepper, adding a splash more wine if it's too thick.
Pour the thickened sauce over the vegetables in the pie dishes.
Brush the rim of each dish with a little milk, then place the pastry lids on top, pressing the edges to seal.
Brush the top of the pastry with more milk and cut a small steam vent in the centre of each pie.
Bake in the preheated oven until the pastry is risen and golden brown – about 10-15 minutes for small pies or 35–45 minutes for a large one.
Serve immediately and enjoy.
Don't skip scraping the bottom of the pan when frying the onions and potatoes. Those browned bits, known as fond, add a huge depth of flavour to the final sauce.