Melt butter and sugar in a frying pan until they form a golden-brown caramel.
Cook pear halves in the caramel until caramelised and set aside.
Pulse flour, butter, and sugar in a food processor until the mixture looks like breadcrumbs.
Add the egg and pulse until the mixture forms a dough, adding milk if needed.
Form the dough into a ball, wrap in film, and chill in the fridge for 40 minutes.
Preheat the oven to 180°C.
Roll out the pastry, line a 20cm tart tin, and bake for ten minutes until golden.
Mix butter and sugar in a bowl until light and fluffy.
Beat in the eggs one at a time until fully incorporated.
Combine the lemon zest, flour, and ground almonds into the mixture.
Spoon the filling into the tart shell and press the pears halfway into the mixture.
Bake for 30 minutes until the filling is cooked through.
Boil and simmer butter, sugar, chocolate, cocoa, vanilla, and 125ml water for 15 minutes.
Serve tart slices topped with chocolate sauce and a drizzle of double cream.