Put the flour, egg yolk, butter and salt in the food mixer and then add the water.
Mix the pastry dough for about 2 minutes and transfer to a work surface.
Knead by hand until you get a smooth dough, wrap in cling film and leave in the refrigerator for about 40 minutes.
Now make the caramel.
Wash and peel the peaches and leave them in the sugar for a moment.
Then take a thick-bottomed saucepan and put in the sugar (removing the peaches), water and butter.
Put on the stove on a medium-high heat.
Once the sugar syrup comes to the boil, it is essential not to stir it at all to avoid crystallizing the sugar.
With a damp pastry brush, you can delicately remove any little splashes that may form on the sides of the saucepan.
When the syrup reaches 170°C the sugar will begin to caramelize and this is when you can rotate the saucepan a little to mix it.
Continue cooking, taking care that the caramel doesn’t darken too much as otherwise it will become bitter.
When it is ready, take a pie dish and put the caramel on the bottom, then place the peaches neatly in a wheel shape and finally the shortcrust pastry, which you will have already carefully rolled out.
Bake in a preheated oven at 160°C for about 30 minutes.
The pie is ready once the pastry is golden.
Serve still warm with vanilla ice-cream or cold, garnished with slices of fresh peach and a few leaves of mint, as you prefer.