Prep: Remove the puff pastry from the freezer and thaw according to package directions. Preheat the oven to 400F and set a lined baking sheet aside.
Cook the Apples: Melt the butter over medium heat in a medium pan. Add the apples to the pan along with the brown sugar, water, cinnamon, ginger, cardamom, nutmeg, and salt. Mix well until the apples are evenly coated in spice. Sauté for 7 to 10 minutes, stirring occasionally, until the apples are tender and there is liquid on the bottom of the pan.
Thicken the Filling: dissolve the cornstarch in water, add to the apples, and stir rapidly. Remove the apples from the heat and set aside while you prepare the puff pastry.
Cut the Puff: Lightly dust a cutting board or large surface with half of the flour, then place one sheet of puff pastry on top. Use a rolling pin to roll the pastry out into an 11″ by 11″ square, then cut into four equal squares.
Fill the Pastry: Fill one half of each pastry square with the cooked apple mixture, leaving a 1/2″ border on the edges. Brush the edges of the pastry with milk, then fold the other half of the pastry over to form a triangle; use a fork to pinch the edges together, then transfer to the baking sheet. Repeat steps 4 and 5 until you have 8 turnovers.
Bake: Cut 1-2 small slits in the top of each pastry with a knife to allow for ventilation, then brush the tops of each pastry with the remaining plant-based milk. Bake in the middle rack of the oven for 20 to 22 minutes, until the pasty is golden brown. Remove from the oven and let cool slightly on the baking sheet.
Make the Glaze (optional): Add the powdered sugar to a medium bowl and add 1 tablespoon of milk; mix well. If the mixture is too thick, add more milk in 1/2 teaspoon increments, until the glaze reaches your desired thickness.
Glaze & Serve: Drizzle the glaze over the turnovers, then serve warm; leftovers will keep at room temperature for up to 3 days or can be frozen for up to 2 months. Reheat leftovers in the oven or toaster oven.