Put the flour, sugar and salt in a bowl, add the butter in the center and start kneading with your fingertips, until you get a crumbly mixture, then add the water, possibly cold from the fridge, and work quickly until obtain a homogeneous dough.
Cover with cling film and let it rest in the fridge for at least 1 hour.
In the meantime, gently wash the blackberries, dry them even more delicately, then mix them with sugar and cornstarch.
Take back the dough, spread it on a sheet of parchment paper in a round sheet of about 2-3 mm thick, then move it into the mold, pour the blackberries in the center and fold the edges over the fruit.
Beat the egg with the milk, then brush the edges of the galette, then pour the leftover egg over the blackberries.
Bake in a preheated convection oven at 180 ° C and cook for 40 minutes.
The blackberry cake is ready, let it at least cool, then decorate with very little icing sugar and serve.