Melt the butter with the sugar in a large frying pan and cook until the sugar has dissolved and the mixture has become a golden-brown caramel.
Add the pear halves and cook, turning once, until caramelised all over. Remove from the heat and set aside.
For the pastry, place the plain flour, butter and sugar into a food processor and pulse together until the mixture resembles breadcrumbs.
Add the egg and pulse until the mixture just comes together as a dough. Add a little milk if required.
Remove the dough from the food processor and roll to form a ball. Wrap in cling film and chill in the fridge for 40 minutes.
Preheat the oven to 180C/350F/Gas 4.
Remove the dough from the fridge and unwrap. Roll the pastry out on a clean, floured work surface to line a 20cm/8in tart tin. Transfer to the oven to bake for ten minutes, or until golden-brown.
For the filling, mix the butter and sugar together in a bowl until light and fluffy.
Add one egg at a time to the butter mixture and mix well, before adding the next (this can be done in a food mixer) until all the eggs are mixed into the butter and sugar.
Add the lemon zest, plain flour and ground almonds and mix well to combine.
Spoon the filling into the baked pastry tin and press the caramelised pear halves into the filling, so that they are half-submerged.
Transfer to the oven and bake for 30 minutes, or until the filling is cooked through.
For the chocolate sauce, place the butter, sugar, chocolate, cocoa powder, vanilla extract and water into a clean pan over a medium heat. Bring to the boil and simmer for 15 minutes, stirring regularly, until the sauce is thick and glossy.
To serve, cut a piece of tart and place on a serving plate, top with the chocolate sauce and drizzle over the double cream.