Preheat the oven to 350F. Line two baking sheets with parchment paper or baking mats.
Mix together the flour, baking soda, salt, and cornstarch together. Set aside.
Beat the butter and sugar together until light and fluffy. Add the eggs in one at a time, and beat well after each addition.
Add in the vanilla and lemon zest and beat until well incorporated.
Add the flour mixture into the butter mixture and mix until just combined.
Roll balls of dough that are 1 ½ tablespoons big and roll in the sugar. Evenly space on the baking sheets. Gently press for less fluffy cookies (if desired).
Bake for 8 - 10 minutes, or just until the edges start to get color.
Leave on the baking sheets for about 2 - 3 minutes before transferring to a wire rack to finish cooling.
Once the cookies are cool, Turn over half the cookies and spread the cake batter frosting on the bottoms of the cookies. Top with the remaining cookies.