Preheat the oven to 180 C / Gas 4. Sprinkle a non-stick baking tray with a tablespoon of brown sugar. Peel the pear, cut it into 6 to 8 quarters and remove the core. Arrange the pear pieces on the sugar. Sprinkle the pear with the rest of the brown sugar. Bake until the pear is tender and caramelised, 20 to 30 minutes. Remove the baking tray from the oven and let cool.
Make the ganache
Beat egg yolks and sugar in a bowl till white and fluffy.
In a saucepan bring the cream to the boil. Add 3 to 4 tablespoons of the cream to the yolks. Stir well then transfer the yolks to the saucepan.
Cook over low heat for 1 to 2 minutes, stirring constantly. Remove from heat before it starts to boil.
Place chocolate in a heat proof bowl. Pour the egg and cream mixture over it, wait for it to melt, then stir until smooth.
Bring the water to the boil. Add the cocoa mixture and stir well. Add this mixture to the chocolate mixture and stir well. Let it cool then refrigerate until using.
Make the sponge
Preheat the oven to 180 C / Gas 4. Line a baking tray with greaseproof paper. In a bowl, beat egg yolks and sugar in a bowl till white and fluffy.
In another bowl, beat the egg whites until stiff, adding a pinch of salt.
Incorporate 1/3 of the egg whites into the yolks. Add the cocoa and mix well. Incorporate the rest of the egg whites by folding them in gently with a spatula.
Tip the mixture onto the prepared baking tray. Even out the surface and bake for about 10 minutes. Check for doneness by inserting a knife, it should come out clean. Remove from the oven and pull the sponge off the baking tray onto a wire rack. Cover with a clean tea towel and let it cool.
Make the syrup
In a small saucepan, heat the water. Add the sugar and vanilla. Leave to cook till thickened for a few minutes. Remove from heat and let cool. Add the cognac and stir.
Assemble the cake
Carefully remove the paper from the sponge. Brush the sponge generously with the syrup.
Spread half of the ganache over the sponge. Place 3 pear pieces on one end.
Roll up the sponge a bit and add 3 more pear pieces. Continue to roll up the sponge all the way. Place it seam side down on a serving plate.
Spread the rest of the ganache all over the cake. Let the log rest in the refrigerator for at least 3 hours. Before serving, sprinkle with cocoa and decorate with macaroons, meringues or other decoration of your choice.