Preheat the oven to 180°C.
Butter and line a loaf pan with parchment paper.
Combine the icing sugar, flour, ground almonds and chestnut flour together. Whisk the egg whites with the salt until firm and they cling to the end of the whisk, then incorporate the sugar and whisk to form a meringue. Fold the dry ingredients into the meringue and transfer to a piping bag without a tip. Pipe into the buttered loaf pan. Bake in the oven heated to 180°C for 20 minutes. Cool, unmould and slice into two horizontally.
Smooth vanilla cream
Mix the gelatine and water over a bain-marie to obtain the gelatine mass. Set aside. Make a crème anglaise: Blanch the egg yolks with the sugar in a bowl. Bring the milk and cream to the boil, add the split and scraped vanilla pods. Pour 1/3 of the hot liquid onto the egg yolks and sugar, mix well.
Return cream to the saucepan, stirring continuously over low heat until it begins to thicken and coats the back of a spoon; lift the spoon, tilt on an angle and draw a horizontal line through the cream with your finger. The edges of the line should remain very neat. (Do not allow to boil).
Remove from the heat, add the melted gelatine mass and blend. Strain through a china-cap sieve and cool. Whisk the cream to stiff peaks. Fold the whipped cream into the crème anglaise. Transfer to a piping bag without a tip and set aside at room temperature.
Jellied pear coulis
Heat the 30 g of pear purée with the glucose to 50°C. Add the sugar mixed with the pectin. Bring to the boil. Add the 40 g of cold pear purée and pear brandy, mix well. Refrigerate.
Mix the chestnut paste with the rum. Add the softened butter and whisk until light and smooth. Transfer to a piping bag fitted with a chestnut-vermicelle tip.
Line the loaf pan with parchment paper. Cut off the end of the piping bag containing the smooth vanilla cream; and pipe a 2 cm deep layer onto the base of the loaf pan. Add layer of chestnut dacquoise, freeze for 10 minutes.
Pour a layer of jellied pear coulis into the loaf pan on top of the dacquoise. Return to the freezer for a further 10 minutes.
Finish with a layer of smooth vanilla cream and close the Yule log with the second chestnut dacquoise. Freeze.
Unmould the Yule log and using the piping bag fitted with a chestnut-vermicelle tip cover with chestnut cream.
Finish with milk chocolate discs, squares and candied chestnuts.