Make a well in the centre of the flour. Put the egg yolks, sugar and a pinch of salt in the centre of the well, then add the butter and the water. Mix with your fingertips until the crumb stage. Use more water at your discretion. The dough must be very smooth. Shape into a ball and chill until firm.
Melt the butter in a frying pan.When it starts to sizzle add the sugar all at once. Cook over medium heat, stirring now and then with a wooden spoon until caramelised to a deep golden brown. Cook gently once it starts to colour because it burns easily. This will take about 3 - 5 minutes. Remove from the heat and allow to cool until tepid.
Arrange the apple halves upright in concentric circles to fill the pan. The apples will shrink during cooking so pack it in tightly. Cook the apples over high heat until caramelised, 15 - 25 minutes. Turn the apples over to caramelise on both sides - use a fork. Remove the pan from heat and let cool 10 - 15 minutes.
Roll out the pastry into a round 2.5 cm larger than the frying pan. Roll up the dough around the rolling pin and transfer to the pan. Drape the dough over the pan. Tuck the edges of the dough down around the apples. Bake the tart in the heated oven until the crust is golden brown. 20 - 25 minutes.
Let the tart cool until tepid in the pan then unmould it. Set a serving plate on top of the pan, hold firmly together and invert the two. If the apples stick to the pan, remove and replace on the tart. If any caramel remains, use it on the apples.
Serve with creme fraiche.