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In a medium bowl, combine the flour, baking soda, cornstarch, and salt. Set aside.
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In a separate bowl, mix together the butter and brown sugar. Add the egg and vanilla, and mix until combined.
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Add the butter mixture to the flour mixture, mixing until combined. Cover and chill the dough in the refrigerator for 2 hours.
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Preheat the oven to 325 F. Line two baking sheets with parchment paper. Set aside. In a small bowl,
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Scoop out about 1 tablespoon of dough and roll it into a ball. Place the dough ball in the bowl of sugar and roll it so all sides are covered with. Place the ball on the prepared baking sheet.
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Scoop out about ½ tablespoon of dough and roll it into a ball. Place the dough ball in the bowl of sugar and roll it so all sides are covered. Place at the top of the larger ball to make Mickey ears. Repeat to make a second ear.
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Repeat steps 6 and 7 with the remaining dough, placing the Mickey shaped balls 2-3 inches apart. Aim to have 6 cookies per baking sheet.
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Bake for 10-12 minutes. Let cool for 5 minutes on the baking sheet before transferring to a wire rack to cool completely.