Whisk together flour, cornstarch, baking powder, and salt in a medium bowl. Set aside.
In a large bowl, cream butter and sugar until light and fluffy (3-4 minutes).
Beat in eggs one at a time, then add lemon zest, juice, and vanilla.
Gradually mix in dry ingredients until just combined.
Chill dough for 1 hour.
Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
Roll dough into 1-inch balls, then coat generously in powdered sugar.
Place on lined baking sheets 2 inches apart.
Bake 11-13 minutes until edges are set but centers still look soft.
Cool on baking sheet 5 minutes before transferring to wire rack.
