Make the caramel: in a saucepan over a low heat, melt the sugar, stirring constantly, until you obtain a fairly dark caramel colour. Add 6 or 7 tablespoons of water, then pour a little caramel on the bottom and sides of a 26 cm diameter savarin (ring-shaped) mould.
Open the vanilla pods and scrape out the seeds. Put the milk in a saucepan with the vanilla seeds and pods and bring to a boil. Let it steep for 10 minutes, then strain the milk.
Break the eggs, separating the whites from the yolks. In a bowl, mix the egg yolks with 60 g of sugar and the sifted flour. Pour the milk on top and mix well again, then add the butter cut into pieces.
Beat the egg whites with the remaining sugar, slowly at first, then speeding up to obtain a not-too-firm meringue. Using a spatula, gently fold the meringue into the vanilla cream.
Fill the caramelised mould with this preparation. Place in a bain-marie and put in the oven. Bake for 35 to 45 minutes, then remove the Paris-Deauville from the oven. Let it cool and set aside for at least 12 hours in the refrigerator.
Turn out the Paris-Deauville, using a knife to loosen it from the sides of the pan, and serve.