Whisk the flour, salt, and sugar in a large bowl. Incorporate the butter into the flour using a pastry blender or your fingertips until the mixture resembles coarse crumbs with some pea-sized pieces remaining.

Drizzle the ice water over the mixture and toss with a fork until the dough starts to form shaggy clumps. Press the dough into a disk, wrap tightly in plastic, and refrigerate for at least 1 hour to allow the gluten to relax.

Place the spinach and water in a bowl, cover, and microwave until wilted by half, 3 to 4 minutes. Drain thoroughly in a colander, chop coarsely, and press firmly with a spatula to remove all excess moisture—this is essential for a crisp crust.

Place the squash cubes in a covered bowl and microwave until just tender, about 8 minutes. Drain any liquid and add the squash to the bowl with the prepared spinach.

Heat the oil in a large skillet over medium heat until shimmering. Add the onion and oregano, cover, and cook until the onion is softened and beginning to brown, 5 to 7 minutes.

Stir the onion mixture, cheese, crème fraîche, and vinegar into the squash and spinach. Season generously with salt and pepper to taste.

Roll the chilled dough on a sheet of parchment paper into a 12-inch circle. Mound the filling in the center, leaving a 2-inch border, then fold the edges of the dough over the filling to create a rustic rim.

Bake the galette at 400°F until the crust is deeply golden brown and the filling is bubbling, 30 to 35 minutes. Let it rest for 10 minutes to allow the filling to set before slicing.