First make the dough for the crust. In the bowl of a food processor, combine the flour, salt, and sugar. Pulse to mix it all together. Drop in the cubes of butter, then pulse the mixture about 10 times. Spoon in the water (6 tablespoon at first), then pulse again just a few more times. Open up the bowl and see if the dough clumps together when pressed. If it doesn't, add another spoonful or two of water, pulse a couple more times.

Dump the messy dough carefully on a very long piece of plastic wrap. Gather all the bits and form a rough disk. Wrap and chill the dough for a full hour, at least.

Now make the plum compote filling. In a medium saucepan, combine the chopped plums, with the muscovado and a pinch of salt. Heat everything together on medium (or even medium-high), stirring fairly often so it doesn't catch at the bottom or burn. Let the fruit compote boil until it is jammy and thickened, not syrupy. You want to boil off a fair bit of the water. This can take a good 20 minutes for the fruit to release its juice and boil down. When the compote is jammy, take it off of the heat. Stir in the ¼ cup of butter. Transfer the compote to a bowl and chill it in a freezer to speed up the chilling process. Stir the compote every 5 to 10 minutes until it is cold, but not frozen. When it's cold, you can leave the bowl of compote on the counter until you are ready to use it.

Press the trimmings together to save them, and wrap and chill for later.

When the tart shell has chilled, place it on a large baking sheet. Dock the pastry with a fork, then line it with parchment and fill it with pie weights. Bake the tart shell in the preheated oven for about 25 minutes.

Take the pan out of the oven and carefully lift off the parchment with the pie weights and set them aside to cool. Bake the tart shell again for another 5 to 10 minutes until it begins to look dry.

Remove the blind-baked tart shell from the oven.

Meanwhile, roll the remaining dough fairly thinly and cut out hearts of different sizes. Brush them with the whisked egg.

Stir the tapioca starch into the cold compote and pour it into the blind-baked tart shell, smoothing it out. Top with fanned out slices of plum, don't worry about covering the entire surface. Fill the gaps with the heart cut outs, arranging them decoratively, like in the picture. Sprinkle everything generously with turbinado sugar.

Bake the plum tart for 60 minutes. After about 45 minutes, you might want to reduce the oven temperature to 350ºF. The tart should be quite bubbly and the filling very thick when the tart is baked. The edges should be golden brown.

Let the tart cool overnight before serving, or at least 5 to 6 hours.