Lightly dust a work surface with all-purpose flour. Place 1 pie dough on the work surface and roll out until about ⅛-inch-thick. Cut out 12 rounds with a 3-inch round cookie cutter. Gather the scraps together, shape into a ball, and refrigerate.

Press each round into a well of a mini muffin tin, pressing in the center and working your way up the sides to form a crust in each one. The dough should hang slightly over the edge.

Re-roll the remaining dough. Cut out 6 more rounds (discard any remaining dough) and line 6 more mini muffin wells. Refrigerate while you make the apple filling.

Heat the oven to 375ºF.

Melt 2 tablespoons unsalted butter in a medium saucepan over medium heat. Stir in ¼ cup packed dark brown sugar, 1 ½ teaspoons apple pie spice, ¼ cup of the water, 1 teaspoon lemon juice, 1 teaspoon vanilla extract, and 1 pinch kosher salt. Cook, stirring continuously, until the brown sugar is dissolved, about 30 seconds.

Stir in 2 ¾ cups finely diced apples. Cook, stirring frequently, until the apples are slightly softened but still have a slight bite to them, about 15 minutes. Meanwhile, whisk the remaining 2 tablespoons water and 2 teaspoons cornstarch together in a small bowl until the cornstarch is suspended.

Give the cornstarch mixture another whisk, then pour into the apple mixture. Cook, stirring often, until the filling is glossy and thickened, about 1 minute more.

Remove the saucepan from the heat. Let cool until just warm to the touch, 10 to 15 minutes.

Divide the apple filling between the tart shells (about 1 heaping tablespoon per shell).

Bake, rotating the mini muffin tin(s) halfway through, until the crust is a deep golden brown and the apple filling is bubbly, about 25 minutes total.

Let the apple tarts cool in the pan for 5 minutes. Transfer the tarts to a wire rack. Serve warm or let cool completely.