Roll out the pie dough thin and cut into 12 circles. Place the dough circles into a muffin tin. Press the dough into the bottom and sides. Set aside.
In a food processor, add the pumpkin, dairy-free milk, cornstarch, maple syrup, sugar, salt, cinnamon, ginger, allspice, and vanilla to the food processor. Process until the ingredients are well incorporated and smooth.
Spoon the pumpkin pie filling into each of the lined muffin cups. Fill almost to the top of the crust.
Bake in a 375-degree oven for 25-35 minutes. Until the pumpkin pie filling is set and the crust is slightly golden brown.
Let cool in the muffin tin a few minutes then remove and place on a wire rack to finish cooling.
Top with whipped topping if desired.