Heat the oven to 200C (180C fan, gas mark 6). Get all your ingredients measured out and lined up on the worktop. This is a one-pot filling, so once you start, it's plain sailing.
Melt the butter with the olive oil in a large, deep frying pan or casserole over a medium heat. Tip in the sliced leeks with a good pinch of salt. Sweat them gently for 8-10 minutes until soft and sweet, not coloured. Add the garlic and thyme and cook for another minute until it smells like heaven.
Turn the heat up, add the chicken thighs and fry for 5-6 minutes until the outside is opaque all over. Don't worry about cooking them through here, they'll finish in the oven.
Sprinkle over the flour and stir well so every piece gets coated. Cook for a minute, then pour in the white wine. Let it bubble and reduce by about half, scraping up all the lovely sticky bits from the bottom of the pan.
Pour in the stock, bring to a gentle simmer and cook for 10 minutes until the sauce has thickened enough to coat the back of a spoon. Stir in the cream, Dijon mustard and parsley, then season to taste. Take it off the heat and let it cool for 10 minutes, this stops the pastry going soggy.
Tip the filling into a 1.5-2 litre pie dish. Lay the puff pastry over the top and press it onto the rim to seal. Trim the overhang, leaving a 1cm lip, and crimp it with a fork. Cut a couple of small slits in the middle for steam, then brush all over with beaten egg and scatter with sesame seeds if you fancy.
Bake for 25-30 minutes until the pastry is puffed up and deep golden brown. If it's browning too fast, cover loosely with foil. Rest for 5 minutes before serving, then dish it up with buttery mash and greens. Yum!