Prepare the partridge meat by trimming and cutting it into smaller pieces. Season generously with salt and pepper.
In a large skillet or pot, melt the butter over medium-high heat. Sear the partridge meat until golden brown on all sides. Remove from the skillet and set aside.
Finely chop the onion, carrots, and celery. In the same skillet, sauté the vegetables in the remaining butter until softened.
Sprinkle the flour over the vegetables and stir well to combine. Gradually add the chicken stock, stirring constantly to avoid lumps. Add the thyme sprigs and bay leaf.
Return the partridge meat to the skillet. Add the cranberries. Bring the mixture to a simmer, then reduce the heat to low and cook for 20 minutes, allowing the flavors to meld.
Pour the mixture into a pie dish. Cover the dish with the puff pastry, trimming any excess. Cut slits in the pastry to allow steam to escape.
Whisk the egg and brush it over the top of the puff pastry. Bake in a preheated oven at 400°F (200°C) for 25-30 minutes, or until the pastry is golden brown and puffed up.
Let the pot pie rest for 10 minutes before slicing and serving hot.
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