Step by step recipe:

1. 30 min.
   Prepare the confectioner's custard with 4 egg yolks, 66 g caster sugar, 330 ml whole milk and 25 g cornflour, using the method explained here.
   
   When the custard is cooked, add 2 tablespoons rum, mix well and cover.
   
   Set aside in the refrigerator.
2. 5 min.
   Put into a food-mixer bowl: 300 g flour, 120 g butter, 190 g caster sugar, 10 g Vanilla sugar, 2 eggs, 10 g baking powder and ½ teaspoon fine (or table) salt.
3. 5 min.
   Start kneading and stop as soon as the dough is evenly mixed.
4. 2 min.
   Weigh the dough and divide into 2 unequal parts: 1/4 and 3/4.
5. 7 min.
   Roll out the smaller piece of dough between 2 sheets of cooking parchment into a circle...
6. 7 min.
   ...the size of your tin or mould.
   
   Using 2 sheets of cooking parchment makes it easier to roll out the soft, fragile dough.
7. 1 hour
   Then roll out the larger piece of dough, again using 2 sheets of cooking parchment, into a circle a little larger (by about 1 inch / 2 or 3 cm) than your tin.
   
   Lay both circles, still in their papers, on a baking sheet and refrigerate for at least 1 hour or overnight.
8. 3 min.
   After this, the dough will be firmer and easier to handle.
   
   Take the larger circle out of the fridge, carefully remove the paper and lay the dough in the tin.
   
   Preheat your oven at 360°F (180°C).
9. 4 min.
   Fill the case with the rum-flavoured custard and level the top.
10. 
    Turn the edges of the dough in towards the centre.
11. 2 min.
    Take the remaining circle out of the fridge, carefully remove the paper and lay in the tin like a "lid" on top of the custard filling.
12. 3 min.
    Use a brush to glaze the top of the cake with beaten egg yolk.
13. 3 min.
    If you like, you can decorate the top by marking the dough with a fork. Use a bit of pressure, or the marks will disappear during cooking.
14. 40 min.
    Bake for 40 minutes.
    
    Best eaten cold, the gâteau Basque will only improve if kept for a day or two.