Heat 1tbsp of the olive oil in a heavy-bottomed, large sauté pan. Tip in the sliced leek and gently fry until just soft. Using a slotted spoon, remove the leeks and set aside.
Pour the rest of the oil into the pan. Add the chicken and fry over a medium-high heat for 2-3 minutes to seal all sides. Drop in the potatoes and fry for 2 minutes, stirring occasionally. With the heat still high, pour in 450ml of the stock with the thyme, stirring to scrape up any sticky bits on the bottom of the pan. Lower the heat slightly, then lightly boil, uncovered, for 10 - 15 minutes or until the potatoes are tender. Meanwhile, lightly blanch the asparagus in boiling water for 2-3 minutes, drain, reserve 12 of the tips and chop the rest along with the stalks.
Slacken the cornflour with 1tbsp of water. Stir this into the pan and cook, stirring, for 1-2 minutes to thicken. Stir in the reserved leeks, the chopped asparagus, crème fraîche and some pepper to season. You may not need salt. If more sauciness is needed, stir in the rest of the stock. Leave to cool.
Preheat the oven to 220℃, (200℃ for fan assisted), Gas Mark 7.
Divide the cooled chicken mixture between 4 small, individual pie dishes, or pour into 1 larger family pie dish. Lay the sliced cheese on top of the chicken filling. For the individual pies, divide the pastry into 4 and roll out each piece on a lightly floured surface so its large enough to make a lid for the dishes, with enough to cut off a thin strip of pastry to sit on the rim of each dish. (If making one large pie, roll out sufficient pastry to make one lid, plus the side strips.)
Press the strips of pastry on the rims, brush with water, then lay the lids over the top. Pinch the edges well to seal. Score lines across the top of each lid and make a small hole in the corner of each pie (or in each corner of the pie if making a large one). Brush the pastry with milk.
Place the dishes (or dish) on a baking tray and bake for 15-25 minutes, depending on the size, or until the pastry is risen and golden and the filling is bubbling. Just before the pies are done, re-heat the asparagus tips in boiling water. Place them in the pie holes to serve.
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