Put the flour, sugar and salt in a food processor and pulse a couple of times to blend. Scatter the pieces of butter over the dry ingredients and pulse until the butter is cut into the flour. At first you’ll have a mixture that looks like coarse meal and then, as you pulse more, you’ll get small flake-size pieces and some larger pea-size pieces too. Add a little of the ice water and pulse, add some more, pulse and continue until all of the water is in. Now work in longer pulses, stopping to scrape the sides and bottom of the bowl if needed, until you have a dough that forms nice bumpy curds that hold together when you pinch them. Just before you reach this clumpy stage, the sound of the machine working the dough will change—heads up. Turn the dough out onto a work surface.
To incorporate the butter more evenly and to catch any dry ingredients that might have escaped mixing, separate small amounts of dough from the pile and use the heel of your hand to smear each piece a few inches across the counter. In French this is called fraisage, and it’s the ideal way to finish blending a dough.
Gather the dough into a ball, flatten it into a disk and put it between two large pieces of parchment paper. Roll the dough, while it’s still cool, into a circle about 12 inches in diameter. Don’t worry about getting the exact size or about having the edges be perfect; when you construct the galette, the edges will be bunched up and pleated and they’ll only look prettier if they’re a bit ragged. The dough will be somewhat thick and that’s fine—you want to have a little heft for a free-form pastry.
Slide the rolled-out dough, still between the paper, onto a baking sheet or cutting board and freeze for at least 1 hour or refrigerate for at least 2 hours. (Well wrapped, the dough can be refrigerated for up to 2 days or frozen for up to 2 months.)
When you’re ready to use the dough, leave it on the counter for a few minutes, just so that it’s pliable enough to lift and fold without cracking.
Storing: The dough can be kept in the refrigerator for up to 2 days or wrapped airtight and stored in the freezer for up to 2 months. If you’ve frozen the dough, leave it on the counter to come to a workable texture and temperature.
Take the rolled-out dough out of the freezer or refrigerator, remove the top piece of parchment paper and, if the dough isn’t already on a rimmed baking sheet, move it to one. Leave the dough on the counter while you mix the fruit.
Mix the fruit with the sugar, tapioca or cornstarch, lemon juice, lemon zest, vanilla, ginger, cinnamon and nutmeg. Set aside for 5 to 10 minutes, stirring occasionally, so that the sugar dissolves and you have syrup in the bowl.
Spoon the fruit and the accumulated juices (unless the fruit is absolutely drowning in liquid, in which case you’ll want to either add more tapioca starch or leave some of the syrup behind) onto the galette, mounding the fruit in the center and leaving the 2-inch border bare. Gently lift the border of dough up and around the filling. As you lift the dough and place it against the filling, it will pleat and fold—it’s meant to. Dot the filling with more butter bits, then brush the dough very lightly with a little water and sprinkle it with sugar.
Bake the galette for 45 to 55 minutes, until the crust is deeply golden brown and the juices are bubbling. If the crust is getting darker than you’d like it to, just cover it with a foil tent.