Preheat the oven to 350 F. Line a baking sheet with parchment paper or a silicone baking mat.

In a medium bowl, whisk together the flour, cornstarch, baking soda, and salt. Set aside.

Using an electric mixer or stand mixer fitted with the paddle attachment, beat the butter and cream cheese until light, about 1 minute.

Add the sugar and beat until light and fluffy, about 3 minutes.

Beat in the egg, vanilla extract, and lemon zest, then stir in the dry ingredients until just combined.

Using a large cookie scoop or tablespoon, drop the cookie dough onto the prepared baking sheets.

Bake for about 15 minutes or just until the tops are set and edges are beginning to turn golden brown. I prefer these cookies to be on the gooey in the middle!

Transfer cookies to a cooling rack and allow to cool completely.

To make the glaze, combine the cream cheese, confectioners' sugar, nilk, and any remaining lemon zest. Whisk until well blended and there are no lumps. Add lemon juice to taste. (I usually add about 1 1/2 tablespoons). If glaze is too runny, gradually add more confectioners' sugar until you reach your desired consistency.

Place cooling rack over a sheet of parchment paper or another baking tray, to catch any drips, and drizzle each cookie with glaze. I personally like to cover the entire top.