Sift the flour into a bowl and add 125g sugar and a pinch of salt. Make a well in the centre and fill it with diced butter. Rub together until the mixture is crumbly. Add the egg yolk and water and knead into a ball. Add a little more water if necessary to form a dough. As soon as a ball forms, stop kneading. Wrap the dough in cling wrap and place in the fridge for 1 to 2 hours.
For the filling:
Melt the butter in a 23cm round tin over medium heat. Once the butter is melted, add 80g of the caster sugar and mix well.
Arrange the apples as tightly as possible in a cake tin, rounded side down. Sprinkle with remaining 1 tablespoon sugar and let caramelise for about 12 minutes on medium heat.
When the apples have caramelised and are slightly softened, remove tin from heat. If the apples have shrunk or there are spaces between the apples, carefully bring the apples towards the centre of the tin and try to minimise any space between the apples. Cool slightly as you work on the pastry.
Preheat oven to 200 degrees C.
Unwrap the pastry and place on a floured surface. Roll with a floured rolling pin to a circle about 5mm thick and 3cm larger than the diameter of your apples, about 29cm.
Place the pastry over the apples and tuck under by folding the pastry down around the inner sides of the tin. Prick the pastry all over with a fork.
Bake for about 30 minutes in the preheated oven.
Remove from oven, let cool 10 minutes, then invert onto a serving plate. Enjoy your tarte tatin while still warm, plain or with a scoop of ice cream.