Combine the water, sugar, vanilla and pear brandy. Set aside.
Preheat oven to 200 degrees C. Beat egg whites until stiff. When they are almost stiff, gradually add sugar while beating. Add the egg yolks, beat 5 seconds and stop the mixer. Add the flour and gently stir in.
Cover a baking tray with baking paper. Using a piping bag, draw the sponge fingers. Sprinkle with icing sugar. Bake 8-10 minutes, making sure they don't burn. Let cool on a rack.
Place the sugar in a saucepan and heat over high heat until it melts. Add cream and rum and stir over low heat until smooth. Add 4 pears, peeled and diced, and cook a few minutes to soften. Remove from heat and let cool.
Soften gelatin in a small bowl of cold water. When soft, combine with the milk in a saucepan. When boiling, pour over the broken chocolate. Let sit a minute then stir until smooth. Set aside.
Whip the cream in a food processor. Gently fold in the cooled ganache. Set aside.
Soften the gelatin in a bowl of cold water. Bring the milk to a simmer with the vanilla bean. Whisk the egg yolks with the sugar.
When the milk is just about to boil, strain through a sieve to remove the vanilla bean. Add the gelatine, brandy and pears. Stir in the egg yolks gradually. Let cool.
Whip the cream until stiff. Fold into the egg mixture and set aside.
Very thinly slice the pear, unpeeled. Spread slices on a baking tray, sprinkle with sugar and cook in an 80 degrees C oven for 90 minutes.
In a round cake tin, place a layer of biscuits that have been dipped in the syrup. Top with a layer of chocolate mousse, then caramelised pears, then Bavarian cream. Smooth with a spatula and decorate with pear chips.