Process butter, icing sugar, flour and cocoa until mixture resembles breadcrumbs. Add egg yolk and the water; process until ingredients come together. Enclose in plastic wrap; refrigerate 30 minutes.
Roll pastry between sheets of baking paper until 5mm thick. Freeze 5 minutes. Lift pastry into an 11cm x 35cm (4½-inch x 14-inch) rectangular loose-based fluted tart tin, press into sides, trim edges; prick base all over with a fork. Freeze 20 minutes.
Meanwhile, preheat oven to 200°C/400°F.
Place tart tin on an oven tray; line with baking paper, fill with dried beans or rice. Bake 15 minutes. Remove paper and beans; bake a further 10 minutes or until browned lightly. Cool on tray.
Reduce oven to 180°C/350°F.
Stir chocolate and extra butter in a heatproof medium bowl over a saucepan of simmering water until just melted. Remove bowl from pan; whisk in egg and flour until just combined. Pour mixture into pastry case; smooth surface.
Bake tart 20 minutes or until just set. Cool. Cover; refrigerate 3 hours or overnight.
Meanwhile, make poached pears, Heat juice, honey, the water, sugar and vanilla bean in a medium saucepan over a low heat; cook, stirring, until sugar dissolves. Bring to the boil over a high heat; reduce heat to medium-low. Add pears; cook 20 minutes or until just tender.
Remove pears from syrup with a slotted spoon. Return syrup to the boil over high heat. Boil 10 minutes or until thickened slightly.
Next make honeyed walnuts. Place walnuts on a baking-paper-lined oven tray. Drizzle with honey; toss to coat. Bake at 180°C/350°F for 12 minutes, stirring halfway, until golden. Cool.
Serve tart topped with walnuts and syrup, accompanied with pears.