For the filling:
Heat lime zest, lime juice and cardamom in a small saucepan for 3 minutes. Transfer to a bowl and let cool. Whisk in eggs, cream and sugar. Cover and refrigerate for 2 hours or overnight.

For the pastry:
Pulse flour, sugar and butter in a food processor until mixture resembles bread crumbs (or rub in the butter with the tips of your fingers). Transfer to a bowl.

Whisk together egg yolk, ice water, lime zest and vanilla; stir into flour to make a dough. Add more water if necessary to make a firm, pliable dough, then knead gently for 20 seconds, until smooth. Wrap in plastic wrap and chill for at least 30 minutes.

Preheat oven to 375°F (190°C). Line an 8- or 9-inch (20 or 23 cm) tart pan with pastry and chill again until firm.

bake blind (cover with parchment paper, fill with rice and cook for 10-15 minutes), then remove paper and rice and bake for 5 minutes. Remove from oven and let cool.

Turn oven down to 325°F (160°C). Pour filling into pastry shell and bake for 35-40 minutes, or until set but with a very slight wobble. Let cool, remove tart pan and dust with confectioner's sugar.