Preheat the oven to 180C/350F/Gas 4.
For the pear, place the butter and flour into a food processor and pulse until the mixture resembles breadcrumbs. Add the caster sugar and most of the beaten egg (reserve some to use as an eggwash), pulsing until the mixture comes together to form a soft dough.
Turn the dough out onto a floured work surface and roll out into a thin circle. Place the peeled pear upright in the centre. Draw up the edges and secure at the top, pressing the dough together at the base of the pear stalk and sealing with some of the remaining beaten egg. Brush with the rest of the egg and sprinkle over the cinnamon and sugar. Place onto a baking tray and bake in the oven for 10-12 minutes, or until the pastry is golden-brown.
For the sauce, place the cocoa, water and sugar in a small pan and simmer for 3-4 minutes, stirring frequently, or until the sugar has dissolved and the sauce is smooth and creamy.
To serve, spoon some of the whipped cream onto the centre of a serving plate and drizzle around the chocolate sauce, feathering it with a fork. Place the pear in the centre, and garnish with fresh mint to serve.