Remove puff pastry from packaging and allow to sit at room temperature on a lightly floured surface for 45 minutes to thaw. Do not try to unfold until it has completely thawed or it will break.
Meanwhile, heat rum in a small saucepan over medium high heat and add raisins. Let simmer until raisins have absorbed all of the rum. Remove from heat. Be very careful with this step, as the rum can catch on fire easily.
Peel apples and cut into a small dice. Heat butter in a medium sized pot until it melts and add the apples. Mix in the brown sugar, cinnamon, and salt. Allow to cook for 5 minutes to release the juices. Mix the cornstarch slurry in to the apples to thicken the sauce a bit. Add raisins and mix well. Remove from heat.
Preheat oven to 400º.
Once the puff pastry has thawed, unfold 1 sheet onto a clean work surface (You will use the second sheet as well, just work one at a time). Lightly coat both sides with flour. Use your rolling pin to roll the dough out to about 9x12 inches. Cut the puff pastry into 12 3" squares.
Brush a piece of puff pastry with aquafaba. Place 1 Tablespoon of the filling on the center of the pastry square.
Cut a small hole into a second 3" square piece of pastry (I use mini cookie cutters for this). This will allow the hot filling to vent and the pastry won't pop apart.
Place the cut pastry piece on top of the piece with filling.
Then use a fork (or other tool) to crimp the edges, pushing down and making sure the two layers of dough really meet. Set on a pan lined with parchment paper and continue this process until all pies are assembled, including the second sheet of puff pastry.
Brush the tops of all of the pies with more aquafaba. Sprinkle liberally with coarse sugar.
Bake in the oven for 20 minutes, until the tops are golden. Remove from oven and let cool for a few minutes before serving. These can be stored overnight at room temperature in a sealed container.
Enjoy!