Whisk the flour, cornstarch, baking powder, baking soda, and salt together in a large mixing bowl. Set this aside for now.
Add the butter, sugar, and powdered sugar to another large mixing bowl. Cream the mixture using an electric mixer at high speed for about 90 seconds, or until smooth and fluffy. Add the corn syrup, aquafaba, and vanilla extract. Beat just until fully incorporated, about 30 seconds.
Begin adding the flour mixture to the bowl, beating in about a cup at a time using the mixer at low speed. Continue until all of the dry ingredients have been added and a soft dough has formed.
Gently fold in the sprinkles.
Cover the bowl and chill the dough for an hour.
Preheat the oven to 350°F and line a couple of baking sheets with parchment paper.
Roll the dough into 1 ½ tablespoon balls, then arrange them on the baking sheets, spacing them at least 2 inches apart. Press a few extra sprinkles into the top of each dough ball.
Bake the cookies for 9 to 12 minutes, until they've spread out and puffed up a bit. They should still look a bit underbaked when they're done (Note 2).
Transfer the baking sheets to cooling racks when they come out of the oven. Let the cookies cool on the baking sheets for about 5 minutes, until they feel set, then remove them from the baking sheets and place them directly on the racks to finish cooling.