Add the flour, the cold butter, the caster sugar, almost all of the beaten egg and the salt in a bowl. Using a pastry cutter or two knives, cut the butter in smaller pieces in the bowl.
With a cold hand, quickly combine all ingredients into a cohesive dough, that doesn't crumble. Add a little bit of egg if the dough it too dry, but don't add too much.
If the dough is getting too warm, the butter will melt: cool the dough during the kneading if necessary.
Once combined, flatten the dough into a flat disk, and place the dough in a plastic bag or Saran wrap, and place in the fridge for about 15 minutes.
In the meantime, peel the apples, remove the core and slice into slices about half or third of an inch thick. You want the slices to have a bit of bite when baked. Too thin, and they'll be too soft. Place in a bowl.
Add a bit of lemon juice (to prevent browning of the apples), the sugar and cinnamon.
For the custard, beat the 3 eggs, the milk and sugar together in a smooth mixture. Don't whisk too hard, you won't need bubbles.
Get a 8 inch spring form pie ring, and grease liberally with butter. Preheat the oven to 350℉.
Flour your work space and roll out the dough to be about 2 inches wider than the diameter of the spring bake tin. Place the dough on the bottom, and press the sides up. You won't have to be careful: it is a heavy dough, with a lot of butter. Make sure the bottom and the slides have roughly the same thickness. Close any thin spots or thin areas to prevent spilling.
Add the apple/raising mixture to the dough in the tin. Try and spread out the raisins as much as you can. Pour in the egg/milk mixture.
Place in the preheated oven, and bake for about 60 minutes. It is a heavy pie with a lot of filling, and baking will take a while. The custard should have just set, and the dough should be golden brown.
Let the cake cool for a few minutes and release from the tin. Eat immediately with creme chantilly, or cool completely and eat from the fridge. Reheat in a 350℉ oven for 10 minutes.