To make the poached pears, place the water, sugar, lemon juice and vanilla in a deep saucepan. Bring up to a simmer, stirring to dissolve the sugar. Add the peeled pears and cook at a gentle simmer for 20 minutes until they are tender.

Set the pears aside to cool in the poaching liquid.

To make the pastry, sift together the flour, cocoa powder, icing sugar and salt in a large bowl. Add the cold butter and rub in using your fingertips until it resembles fine breadcrumbs and no lumps of butter remain.

Add the cold vodka (if using) and mix to combine. Gradually add enough cold water to bring the pastry together into a ball. Shape the pastry into a disc (don't knead it), wrap and refrigerate for about an hour until firm enough to roll out.

Roll the pastry out on a lightly floured surface into a circle big enough to line a 23 cm/9 in round pie dish. Press the pastry right into the corners then trim off the excess.

Prick the base of the pastry shell all over with a fork then place it in the freezer for 20 minutes until solid. Meanwhile preheat the oven to 180°C/160°C fan/350°F/gas mark 4.

Line the pastry case with baking parchment, pressing it right into the corners, then fill with baking beans or dried rice, making sure that the sides are propped up.

Bake for 20 minutes then remove the parchment and baking beans and return the tart shell to the oven for a further 5-10 minutes until dry to the touch. Remove from the oven and set aside.

To make the frangipane melt the chocolate and vegan butter together in a large bowl, either over a pan of hot water or in short bursts in the microwave, stirring often.

Whisk in the milk and sugar then sift in the cocoa powder, flour and baking powder and add the ground almonds. Stir with a balloon whisk until well combined.

Pour the frangipane into the pastry case and spread it level.

Drain the pears really well and pat dry with kitchen paper. Slice the pears in half lengthways and use a teaspoon to gently scoop out the core, stem and seeds. Cut slices down the length of the pear half leaving the narrow end uncut. Spread the pear slices to form a fan shape.

Arrange the fanned pears on top of the frangipane, you probably will not need all of them.

Bake the tart for about 50 minutes until a skewer inserted into the centre of the frangipane comes out gunky with moist crumbs, but no wet batter. Allow to cool for half an hour before serving.