In the bowl of a stand mixer, combine softened butter and sugar. Using the paddle attachment, beat the butter and sugar together until pale and fluffy, about 5 minutes. Add the egg and beat mixture for another 1-2 minutes. Add the vanilla extract, lemon juice and lemon zest and beat in for 10-15 seconds.
In a separate mixing bowl, add flour, baking soda, corn starch and salt. Mix so the dry ingredients are incorporated into the flour. Add half of the dry ingredients to the wet ingredients and mix just until combined. Scrap down the sides of the bowl and then add remaining dry ingredients. Mix just until all the dry ingredients are incorporated into the wet ingredients. Do not over mix. Cover dough and refrigerate for one hour or up to overnight.
Preheat oven to 350°F and line a cookie sheet with parchment paper. Use a cookie scoop to scoop the dough. Roll the dough into a ball and then place on the parchment lined baking sheet.
Bake cookies at 350°F for 10-11 minutes. Remove cookies from oven and transfer to a wire cooling rack. Allow cookies to cool completely.
While the cookies are cooling, make the lemon glaze. In a small mixing bowl, add powdered sugar and lemon juice and mix until a thick glaze as formed.
When cookies have cooled, use a butter knife or small rubber spatula to glaze each cookie. Sprinkle each cookie with lemon zest, if desired.