In the bowl of a stand mixer, beat together the butter and sugar until smooth and fluffy, about one minute. Add the lemon zest and juice, mixing until incorporated. Beat in the eggs, one at a time, mixing well after each addition. Mix in the vanilla extract.
In a separate medium bowl, whisk together the flour, cornmeal, baking powder and salt.
Add the dry ingredients to the butter mixture and beat on low speed until just combined. Cover the dough with plastic wrap and refrigerate until cool enough to handle, about one hour.
Preheat the oven to 325 degrees.
Pinch off dough by the tablespoon and roll into balls. Place balls on parchment lined baking sheets and flatten into discs with your hand. Press down gently on the cookies with a fork. Bake for 13-16 minutes, until cookies are pale on top and lightly golden on the bottom. Transfer cookies to a wire rack to cool. Dust with confectioner's sugar.