Cut the chestnuts crosswise on the pointed side and cook in the oven at approx. 180 °C.
Let cool and peel, sort out the bad ones. Melt the couverture in the warm cream, puree the chestnuts and possibly some milk in it and pass through a sieve.
Beat the egg yolks with the sugar, add the milk.
Whip the mixture on the stove or on a water bath to a rose and cool while continuing to beat. Mix both masses together and stir in a cup of double cream. Freeze everything in the ice cream maker.
Crack, clean and coarsely chop the nuts.
Let them caramelize in a pan together with the sugar.
Pour onto a glass board and chop coarsely if necessary.
Peel and core the quince and cut into thin slices. Sauté in a pan together with the sugar. Add the oil and water and let the caramel not become too solid.
Arrange everything together decoratively and serve immediately.