1. In a mixing bowl, cream together vegan butter, 1/2 cup sugar, and brown sugar with an electric mixer until fluffy, about 2 minutes.
2. In a small bowl, mix ground flaxseed and water to make a flax egg. Let sit 5 minutes, then add to the butter mixture with 1 teaspoon vanilla. Mix for 30 seconds.
3. Add 1 1/2 cups plus 3 tablespoons flour, 1 teaspoon pumpkin pie spice, baking powder, and salt to the bowl. Mix until a thick dough forms. It will start crumbly; continue mixing until soft and cohesive.
4. Cover dough with plastic wrap and chill in the fridge for 30 minutes.
5. While dough chills, make pumpkin pie filling: In a bowl, whisk together pumpkin puree, maple syrup, oat milk, cornstarch, 1 teaspoon vanilla, and 1/2 teaspoon pumpkin pie spice until smooth. Set aside.
6. Preheat oven to 350°F and line a baking sheet with parchment paper.
7. Scoop dough into 11 balls. Roll each in 2 tablespoons sugar to coat. Place on baking sheet and gently press each ball down with your palm.
8. Use your thumb to make an indent in the center of each cookie, then widen slightly with your fingers.
9. Spoon about 1 1/2 tablespoons pumpkin filling into each indent, keeping filling within the edges.
10. Space cookies at least 2 inches apart. Bake for 12–14 minutes until edges are crisp and filling is set.
11. Cool on baking sheet 5 minutes, then transfer to a wire rack to cool completely.
12. Once cool, top with vegan whipped cream and a sprinkle of pumpkin pie spice if desired.