Preheat oven to 220 degrees Celsius Heat oil and butter in a heatproof casserole. Add chicken, garlic, leeks/onion, carrot, celery, thyme and cook gently for about 20 minutes. Season, then turn the heat up and sprinkle the flour slowly until everything is coated, then add milk, wine and a glass of water. Turn the heat down and simmer for half an hour, checking every so often to make sure it doesn't stick. If it is still too liquid, give it a bit longer.
Stick the mixture in an ovenproof dish. (I like those old-fashioned enamel ones) Roll out the puff pastry over the dish, and trim the edges. Use the trimmings to cut out pastry hearts and kisses or your loved ones initials. Paint the pastry with the beaten egg, then score it in criss–cross lines. Stick your hearts, kisses, names on the top and egg wash them too.
Bang it in the hot oven for about 35 minutes until its a lovely golden brown and your endearments are all puffed up proud on the top. If it is especially cold, do a big dish of buttery mash too, and if it is just a teeny bit Autumnal, I'd go for a big floury baked potato to mop up the juice and some emerald green broccoli spears.