Prepare the chicken:Preheat the oven to 425°F (220°C). Take a large casserole pot and add your olive oil and butter.
Add the chicken, leeks, carrots, celery, and thyme and cook slowly on the stove for 15 minutes. Turn the heat right up, add the flour, and keep stirring for a couple of minutes before adding the wine, a wineglass of water, and the milk. Season with a little salt and freshly ground black pepper, then cover with a tight-fitting lid and simmer very slowly on the stove for 30 to 40 minutes until the chicken is tender. Stir it every so often so it doesn't catch on the bottom of the pan. The sauce should be loose but quite thick. If it's a little too liquid, just continue to simmer it with the lid off until it thickens slightly. (At this point you can let it cool and keep it in the fridge for a couple of days if you want to — it can also be eaten as a stew.)
Assemble the pie: Pour the chicken mixture into an appropriately sized pie dish. Squeeze the meat out of the sausage skins, roll it into little balls, brown them in a little oil and sprinkle them over the stew.
Roll out your pastry to about 1/4 inch thick. Egg-wash the rim of the dish and drape over the pastry, using a knife to trim the edge of the dish. Egg-wash the top of the pastry to make it go golden while cooking, then pinch it to crimp it round the edges (there's no need to do this, but I like to as my mum always does it and it makes it look pretty). I use the back of a knife to lightly crisscross the top — this allows the pastry to go crisp and flaky. Cook the pie in the center of the oven for about 30 to 40 minutes, until golden on top. I like to serve this with corn off the cob and mashed potato.