In a mixing bowl, whisk together flour, cornstarch, baking soda and salt, set aside.
In the bowl of an electric stand mixer fit with paddle attachment, whip together butter, sugar and lemon zest on medium-high speed, until mixture is pale and fluffy, about 3 minutes. Blend in egg, then egg yolk.
Mix in lemon juice and vanilla extract.
Slowly add in dry ingredients and mix just until combined.
Scoop dough out by the heaping tablespoonfuls, form into balls and drop onto Silpat or parchment paper lined baking sheets.
Bake in preheated oven 9 - 11 minutes (for a gooier cookie closer to 9 and a more set, fluffy cookie more near 11).
Allow cookies to cool on baking sheet several minutes before transferring to wire rack to cool. Drizzle cooled cookies with Lemon Glaze (you can do this while they are still slightly warm if desired).
Store in a single layer in an airtight container.
For Lemon Glaze
In a small mixing bowl, whisk together powdered sugar and enough lemon juice to reach a drizzle-able consistency.
Pour mixture into a resealable bag, seal bag and cut a small tip off one corner then drizzle glaze over cookies.
Sprinkle with lemon zest and powdered suger (optional)