1. Remove the pastry from the fridge and let it come to room temperature. Grease and line a 22cm-wide tart tin. Dust your work surface with a little flour and thinly roll out the pastry to make a circle slightly larger than the tin. Use the rolling pin to transfer the pastry to the tin, and carefully press the pastry into the tin to line the bottom and sides. Loosely cover and chill in the fridge for 1 hr.
2. Preheat your oven to 180°C/Fan 160°C/Gas 4. Take the tart case out of the fridge, line it with baking paper and tip in some ceramic baking beans, dried lentils or rice to cover the base. Slide the tin into the oven and bake for 20 mins till the pastry feels a little dry. While the pastry is in the oven, break 1 egg into a small bowl and beat it with a fork. Set aside.
3. When the pastry has baked for 20 mins, remove the tin from the oven and remove the baking beans and paper. Brush the a little of the beaten egg over the bottom and sides of the pastry. Return the tart case to the oven, uncovered, and bake for a further 10-15 mins, till lightly golden brown in colour. Once cooked, set the pastry case aside. Reduce the oven temperature to 140°C/Fan 120°C/Gas 1.
4. While the pastry case bakes, pour the milk and cream into a large pan. Lightly crush the cardamom pods and add them to the pan. Warm the milk and cream till just steaming. While the pan is warming, crack 3 eggs into a large, heatproof bowl. Add the 3 egg yolks, 100g sugar and 1 tsp cornflour. Use a whisk to beat the eggs and sugar together, till thick and light in colour.
5. When the milk mix is just simmering, carefully pour half of the liquid through a sieve (to catch the cardamom pods) into the bowl with the sugar and eggs, while whisking. Whisk till combined and smooth, then pour the contents of the bowl back into the pan. Whisk the pan to fully combine and remove from the heat. Pour through a sieve into a jug to catch the last of the cardamom pods.
6. Very carefully pour the custard into the pastry case, filling it to the top. Transfer the tart to the oven and bake it for 50 mins-1 hr, till the custard filling is just set with a slight wobble in the middle. Once cooked, allow the tart to cool fully, then remove from the tin and serve in slices.