These chewy soft lemon cookies are wonderfully refreshing, with a big burst of lemon in every bite. The fresh lemon icing is simply divine; a must-do for these cookies! Cookies stay chewy for days if wrapped airtight. Dough can be made ahead and chilled until ready for use.
Preheat oven to 350F, with rack on lower middle position.
In a bowl, whisk together the flour, cornstarch, baking soda, and salt until well combined. Set aside.
In the bowl of a stand mixer, blend together the butter, sugar, and zest on medium high speed using paddle attachment. About 3 minutes, or until mixture is light and fluffy. Add egg and egg yolk, and blend just until combined. Add lemon juice and vanilla extract. Blend until combined.
Using a rubber spatula, fold dry ingredients together with the wet ingredients. Fold together until no dry lumps remain and dough comes together in one big ball.
Wrap dough tightly in plastic wrap and chill 1 hour or longer. (At this point, dough can be chilled for a day or two before using.)
Line baking sheets with parchment paper. Form dough balls about 1 inch round, and place 2 inches apart on parchment. Bake 8-9 minutes or just until cookie looks puffy and light golden. It will seem slightly underdone, but they will set upon cooling. Do not over bake.
Allow cookies to cool on baking sheets until they are cool enough to transfer to wire rack.
While cookies are cooling, make the icing. In a small bowl, whisk together the icing ingredients. If too thick, add a bit more lemon juice. If too thin, add a bit more powdered sugar. Transfer to a Ziploc bag, seal it, and cut a tiny hole in corner tip. Drizzle over cookies. Once set, the icing will be firm enough to stack cookies on top of each other.