Put the butter, salt, flour and cold water in the mixing bowl of your food processor. I also added grated vanilla pods. Knead for 20 seconds, flip the dough onto plastic wrap, shape into a ball, and chill for at least 30 minutes before you start to work with it.
The secret to a soft dough is that it should not be overmixed, which is why you should avoid excessive kneading by hand, which can heat the dough up.
For the plum filling:
Put the plums in a saucepan. Add the sugar, cardamom seeds, a teaspoon of cinnamon and a splash of white rum near the end of cooking. Leave on low heat until the rum evaporates, 2-3 minutes, stirring often.
Assemble and serve:
Roll out a round sheet of dough and transfer it to a baking tray lined with parchment paper. Place the plum filling in the middle of the sheet, leaving 7-8 cm (about 3 inches) of dough around the plums. Bring the edges of the dough towards the center, partially covering the plums.
Brush the dough with egg, sprinkle with sugar, and bake the plum galette for 25 minutes at 180° C/356° F.
After baking, serve warm with a scoop of vanilla ice cream. You can also sprinkle a few nuts on top.