Step 1: Prepare the puff pastry tart shells. Heat the oven to 350°F and spray the muffin tins with non-stick spray or brush with melted butter. Unfold the pastry sheet on a lightly floured surface and roll out into an 18"x9" rectangle (you will double the length of the 9x9" sheet). Cut into 18 squares *see photo for reference. Whisk the egg with the water to make the egg wash. Press the pastry squares into 18 muffin-pan cups.
Step 2: Make the filling. In a medium saucepan, melt the butter over medium-high heat. Add the apples and cook for 3-4 minutes until they start to soften. Stir in the sugar, spices, and cider, bring to a simmer, and cook until the apples are soft and the liquid begins to reduce, about 3 to 4 minutes more. In a small bowl, whisk together the water and cornstarch and add it to the pan. Cook, stirring, until the mixture thickens, about 1 more minute. Remove from the heat and let cool. (You can do this step in advance for faster prep.)
Step 3. Make the crumble. In a medium bowl, prepare the topping by stirring together the oats, flour, maple syrup, cinnamon, and salt. Cut in peanut butter and butter with a pastry blender until mixture resembles coarse crumbs.
Step 4. Assemble the tarts. Using a pastry brush, lightly brush the sides and edges of the pastry dough with the egg wash. Spoon the apple filling evenly into the tart shells and top evenly with the PB crumble (about a tsp per tart).
Step 5. Bake. Bake the tarts for 15-20 minutes, until lightly golden brown. Allow the tarts to cool for a few minutes before removing from the pan. Enjoy with a dollop of whipped cream or vanilla ice cream. You can also garnish with a sprinkle of cinnamon or powdered sugar.