To make the crust, mix the flours, sugar, and salt in a large mixing bowl. Add the butter and use a pastry cutter or two knives to cut the butter into the flour, until the pieces of butter you have in the mix are about the size of peas (alternately, you can put the flours, salt, and sugar into a food processor, add the butter, and pulse until the ingredients are combined and the butter is the size of peas).
Mix the ice water and vinegar. Add the water into the flour mixture in a thin stream, using a spatula to mix as you go. As soon as the dough holds together without being wet or sticky, and it sticks together when you squeeze a small amount in your hand, it's ready. If your dough is too crumbly and isn't holding together, add additional ice water by the teaspoon until it does. Transfer the dough to a floured work surface and shape it into a disk. Wrap it in plastic wrap and refrigerate for at least 1 hour. At this point, you can keep the dough in the fridge for up to 2 days or freeze it for later use, if you like.
When the dough has finished chilling, preheat your oven to 400F. Toss together the plums, sugar, salt, lemon, and flour. Flour a work surface and roll the dough into a circle that's about 12-14 inches across and 1/4 inch thick. Carefully transfer this circle to a parchment-lined baking sheet.
Pile the plum mixture into the center of the galette, leaving about 1 1/2 inches of dough free all around the sides of the circle (you'll fold these over the filling). Don't worry about making any pretty patterns with the fruit, unless you'd like to. A rustic look is the goal!
Fold the edges of the galette over the filling. You can be as casual or as neat as you want to be here, so long as the fruit gets tucked into the dough. If you like, whisk together the non-dairy milk and syrup, then brush the folded sides of the galette with the mixture and sprinkle them liberally with demerara sugar.
Bake the galette for 40-50 minutes, or until the crust is a deep, golden brown and it's sturdy all the way around when you tap it (I recommend checking in on it at 35 minutes, just to see where you are). Allow the galette to set in a cool, dry place for at least a couple hours (3-4 is ideal) before slicing and serving. Top with vegan ice cream, whipped cream, or enjoy it the way it is!