Pour the flour, confectioners’ sugar, and salt into the bowl of a food processor and pulse to combine. Add the diced butter and pulse about 10 times to break it up. With the machine running, add the beaten egg and process until the dough begins to form a mass on the blade, about 15–30 seconds.
Dump the dough onto a clean (not floured) work surface, gather it into a ball, and knead briefly to ensure everything is incorporated. On a lightly floured surface, roll the dough into a 13-inch (33 cm) circle. Transfer the dough to a rimless, parchment-lined baking sheet and chill in the fridge while you prepare the blueberry filling.
Preheat the oven to 425°F (218°C). Place the blueberries in a medium bowl and sprinkle them with granulated sugar, cornstarch, and lemon zest. Stir gently with a spatula to coat.
Sprinkle the tapioca granules over the dough, leaving a 1 1/2-inch (4 cm) border all around; this will help ensure the galette isn’t runny with juice. Mound the berry mixture onto the pastry dough and spread it out with a spatula, leaving a 1 1/2-inch (4 cm) border around the edge.
Fold the edge of the dough over the filling, creating pleats as you go. Brush the edge with the beaten egg and sprinkle with Demerara sugar.
Bake until the crust is beautifully golden, about 25 minutes. Serve warm or at room temperature, with or without whipped cream or vanilla ice cream.