To make the crust, combine the vinegar and water. Place the flour and salt into a food processor fitted with the S blade. Pulsing constantly, drizzle in the olive oil. The mixture should be crumbly but not yet sticking together. Pour in the water, tablespoon by tablespoon, pulsing as you go, until the mixture is starting to clump together. Shape it into a ball, then flatten it into a disk. Wrap in plastic wrap and refrigerate for 30 minutes or up to 2 days. (You can also do this process by hand, using a pastry cutter or 2 forks.)
To make the galette, preheat your oven to 375F. Flour your work surface and roll the crust dough into a circle that's about 12-14 inches across and ¼ inch thick. Carefully transfer this circle to a parchment-lined baking sheet. Spread the herbed cashew cheese in the center, leaving about 1 1/2 inches of crust at the edges.
Toss the sweet potatoes with the oil and thyme, along with a generous pinch of salt and black pepper to taste. Pile the sweet potatoes on top in an overlapping, circular pattern on top of the cashew cheese (don't be afraid to pile them up at the center!). If you have leftover potatoes, you can roast them on a separate tray alongside the galette.
Bake the galette for 40-50 minutes, or until the crust is a deep golden shade and the potatoes are entirely tender. Allow it to cool to room temperature on a cooling rack before slicing into wedges and serving.