Heat the oven to 350°F and line a standard 12-cup muffin pan.
Whisk the flour, cornstarch, baking powder, baking soda, and pumpkin pie spice in a medium bowl.
Whisk the pumpkin puree, evaporated milk, sugar, and eggs in a large bowl until smooth.
Stir the dry mixture into the pumpkin mixture in two additions, mixing just until no dry patches remain.
Divide the batter among the liners and bake for 30 to 38 minutes, until the centers are set and a toothpick comes out clean or with moist crumbs.
Cool for 10 minutes in the pan, transfer to a rack, cool completely, and finish with whipped topping.