For shortcrust pastry
110g cold butter
1 egg yolk
3-5 tbsp ice-cold water
For poached pears
6 pears, peeled, halved and cored
1/2 vanilla bean
a few strips of lemon peel
juice of 1/2 a lemon
For brown butter and cardamom filling
1/2 tsp ground cardamom
pinch of salt
Make the shortcrust pastry
1. Cut the butter into cubes and rub into the flour with your fingertips. Keep everything as cold as possible. Stop when the mixture looks like coarse breadcrumbs. Add the egg yolk and enough water to just bring the dough together so it holds. A slightly drier pastry will yield a crisper, more crumbly crust, although it will be a bit more difficult to roll out.
2. Collect the pastry into a ball, wrap in plastic wrap and chill in the fridge for at least one hour.
3. On a floured surface roll the dough out slightly larger than the 30-centimetre fluted tart tin. Trim the pastry slightly above the edge of the tin to allow for shrinkage during cooking. Freeze the case or chill well until you are ready to bake.
4. Use baking paper and pie weights or dried beans to weigh down the tart case as it bakes. Bake at 180C for 10-15 minutes then remove the weights and bake for a further 5-10 minutes until the shell is golden. Cool and set aside.
Poach the pears
5. In a non-reactive saucepan bring the sugar and water to the boil with the vanilla bean (split lengthwise and seeds scraped into water) and lemon rind. Put the pear halves into the syrup, add the lemon juice, cover with a square of greaseproof paper to keep the pears submerged, and put the lid on the saucepan. Simmer until the pears are just soft, about 15 minutes, then remove from the syrup and chill. The pears, returned to the cold syrup, can be kept in the fridge for a few days.
Assemble the tart
6. Slice each poached pear half into six pieces and arrange in a circular pattern in the prepared pastry case.
7. To make the filling, whisk together the sugar and eggs until lightened in color, then whisk in the flour, cardamom and a pinch of salt.
8. Brown the butter in a small saucepan over a low heat until dark brown. Remove from heat and allow to cool slightly but whisk into the egg mixture while still very warm. Pour this filling over the tart as soon as possible and bake at 175C for about 45 minutes. The filling should be close to fully set before being removed from the oven.
9. Serve warm or cool with a dollop of lightly sweetened whipped cream.