Preheat oven to 350 degrees.
In your mixing bowl, whisk together flour, cornstarch, baking soda and salt, set aside.
In the bowl of an electric stand mixer fitted 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 dough into balls and drop onto a parchment paper lined baking sheet. With the bottom of a glass, gently "flatten" the dough ball.
Bake cookies in preheated oven for 9 - 11 minutes (for a gooey centered 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 slightly warm cookies with **Lemon Glaze.
Store in a single layer in an airtight container.
**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 slightly warm cookies. Alternatively, you can use a spoon. Allow glaze to set at room temperature.
Store in an airtight container.