Preheat the oven to 200C/400F/Gas 6.
For the pastry, place the flour and butter into the bowl of a food processor and blend until the mixture resembles breadcrumbs. Add the egg and sugar and water to the bowl and blend again until the ingredients have formed a dough.
Bind the dough together with floured hands and roll it out on a floured surface to a thickness of 1cm/½in. Cut into a 25cm/10in circle.
For the filling, place the butter and the sugar into an ovenproof frying pan that is a little smaller than the pastry circle. Heat the ingredients until they have melted and combined.
Add the pear, chestnuts and chilli and mix well. Fry the mixture for four minutes.
Place the pastry onto the mixture in the pan and press the edges in tightly onto the pan.
Place the frying pan into the oven and bake for ten minutes.
To serve, turn the tarte out onto a clean plate and serve with the ice cream alongside.