In a food processor, mix the flour, sugar, and salt. Pulse to combine.
Add the cold vegan butter cubes and pulse until the mixture resembles coarse crumbs.
Add the ice water, one tablespoon at a time, pulsing until the dough starts to come together.
Remove the dough from the food processor. Gather the dough into a ball, wrap it in plastic wrap, and refrigerate for at least 30 minutes.
In a large bowl, toss the thinly sliced apples with sugar, lemon juice, cinnamon, nutmeg, and cornstarch. Set aside.
Preheat the oven to 400°F. Line a baking sheet with parchment paper.
Roll out the chilled dough on a lightly floured surface into a rough circle about 12 inches in diameter.
Transfer the dough to the prepared baking sheet.
Arrange the apple slices in the center of the dough, leaving a 2-inch border around the edges.
Fold the edges of the dough over the apples, pleating as you go to create a rustic edge.
In a small bowl, mix the almond milk and maple syrup. Brush this mixture over the crust. Optional: Sprinkle with coarse sugar.
Bake the galette for 35-40 minutes or until the crust is golden and the apples are tender.
Let the galette cool for 10-15 minutes before slicing. Serve as is or with a scoop of vegan vanilla ice cream!