Beat the butter, sugar and eggs with an electric mixer until light and fluffy. Stir in the cornstarch, flour, grated chocolate and baking powder and mix until smooth.
Peel the pears, cut into quarters and remove the cores. Slice 2 of the quarters thinly and dice the rest. Place the water, sugar and diced pears in a saucepan and bring to a boil. Simmer for 2-4 minutes, until the pears are tender. Remove from heat, stir in the rum and fold into the batter. Pour the batter into a greased springform pan and arrange the pear slices on top.
Bake in an oven preheated to 200°C (approximately 400°F) for 60-70 minutes, until a toothpick inserted comes out clean. Remove from the oven and let cool slightly before loosening the springform pan. Dust with powdered sugar, slice and serve.