1-First, start by preparing the filling to capture that classic apple pie essence. Whisk cold water with cornstarch until smooth, then in a saucepan, combine the apple pieces, brown sugar, vegan butter, lemon juice, and pumpkin-pie spice. Cook over medium heat while stirring until the butter melts and the mixture bubbles, then stir in the cornstarch slurry and continue cooking for 5-10 minutes until thickened.

2-Next, move on to the spiced cookie dough. In a large bowl, mix the softened vegan butter, granulated sugar, and brown sugar until light and fluffy, then add the flax egg and vanilla, mixing for about 30 seconds. Stir in the flour, baking powder, pumpkin-pie spice, and salt until a thick, cohesive dough forms, and cover it to chill for 30 minutes to 1 hour.

3-Finally, assemble and bake the cookies. Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper. Scoop the chilled dough into 10 even balls (about 2 tablespoons each), roll each in the reserved 2 tablespoons of granulated sugar, place on the sheet, and gently press flat. Create a shallow indent in the center of each cookie and spoon about 1 tablespoon of the cooled apple-pie filling into each. Space them about 2 inches apart and bake for 14-16 minutes, or until the edges are lightly crisp and the centers are set. Let them cool on the sheet for 5 minutes, then transfer to a wire rack.