Prepare the filling: In a large mixing bowl, cream the coconut sugar with the vegan butter until soft and fluffy. Add the almond flour, cornstarch, almond milk, applesauce, almond extract, and vanilla extract. Mix using a wooden spoon or spatula until well combined. It won't look smooth and will be thick because of the almond flour, this is normal. Set aside.
Line a baking sheet with parchment paper. Unroll your puff pastries and cut them into about 8 inches discs. Place one disc of pastry on your prepared baking sheet.
Spread the almond filling on top of the disc of pastry, leaving about one inch of the border exposed. At this step, you can place a whole almond or a "fève" in the almond filling. The person who will find it will become the king or queen!
Place the second disc of pastry on top and seal the filling by pressing the edges with your thumb. Using a knife, flute the edges as shown in the photos. Next, make a hole in the center of the top disc of pastry, this will prevent the galette from rising too much.
Brush the top of the galette with the maple syrup wash (try to avoid the edges as it might prevent them from rising well) and draw a pattern using a sharp knife.
Refrigerate for 30 minutes. In the meantime, preheat oven to 350°F (175°C).
Remove from the refrigerator and brush it a second time. Using a fork or small knife, poke small holes in the top. Again, this will prevent it from rising too much and allow the steam to escape during baking.
Bake for 30-35 minutes, or until golden brown. Let cool at least 35 minutes before serving.
This galette can be served at room temperature or slightly warm. I found out it tastes even better the next day as the flavors have time to merge and the filling to firm up slightly.
This Galette des Rois will keep for up to 3 days at room temperature, covered with aluminum foil.