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1
Roll the puff pastry to 4 mm thickness. Cut two circles of 12–15 cm diameter. From the second circle, cut a smaller circle from its centre, producing a ring. Place the base circle on a lined baking sheet. Brush its perimeter with egg wash and press the ring firmly on top, forming the walls of the case. Egg-wash the upper surface of the ring, taking care not to let wash run down the cut sides. Chill the assembled case until firm to the touch.
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2
Bake at 210 °C for 25–30 minutes. The case must rise magnificently and colour to a deep, thoroughly golden brown — bake slightly darker than instinct suggests, as it will soften from the filling's steam. Once baked, scoop out the soft interior pastry to create a hollow vessel. Set the case and its lid aside in a warm place.
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3
Melt the butter in a heavy saucepan over a moderate heat and stir in the flour to form a light roux. Cook the roux briefly without colouring, then add the combined chicken poaching liquid and mushroom cooking liquor in a thin stream, whisking constantly. Cook gently for 20 minutes, stirring regularly, then strain through a fine sieve. The velouté should coat a spoon cleanly.
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4
This is where the dish lives or dies: beat the egg yolks with the cream in a bowl. Ladle a measure of the hot velouté into the liaison, whisking to temper, then pour the tempered mixture back into the sauce off the heat, stirring to combine. Do not return the sauce to a boil. The finished sauce must flow — rich and silken, not stiff — and must coat a spoon in a smooth, unbroken film.
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5
Fold the diced poached chicken, mushrooms, and quenelles or sweetbreads (if using) into the warm sauce. Taste and correct seasoning. The ragout should flow slightly when stirred — if it holds its shape like a paste, it is too thick.
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6
Spoon the warm filling into the warm vol-au-vent case until generously filled. Set the pastry lid at a jaunty angle on top. Serve immediately: the contrast between the shattering pastry and the silken ragout is the entire joy of the dish.