Put the flour, salt, and sugar in a large bowl.
Add the butter pieces, and pinch with the fingers to create a crumb texture.
Make a well in the middle, and pour in the water and vanilla.
Quickly work in the flour to create dough.
Do not over-mix.
Divide into 2 disks, wrap in plastic, and refrigerate 15 minutes before rolling out.
Roll one of the pastry disks into a rectangle and lay on a baking sheet.
Lay down a cobblestone alley of whole plumbs, leaving a 1-inch/2.5 cm margin all around.
Cut the remaining plums to fill in any gaps.
Sprinkle over the sugar.
Roll out the second disk of dough into a larger rectangle.
Lay over the plums and seal the edges.
Trim the edges.
Cut two slits in the top of the tart.
Paint all over with the beaten egg white so the tart will emerge glossy.
Bake at 400ºF/200ºC until the pastry is done, about 25 minutes.
The plum juices will have spilled out all over the baking sheet.
Dip a pastry brush into them and paint the tart all over a glossy violet.
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