Combine butter and cream cheese in a bowl fit with a paddle attachment of a mixer. Cream together for about 1 minute.
Add granulated sugar and continue to mix. Add egg and vanilla extract and continue to beat on medium to high speed until light and fluffy, about 5-7 minutes.
Add half the flour, all the baking soda, salt, cornstarch and lemon zest. Add lemon juice and the remaining flour.
Mix to combine until the dough starts to form like a ball. Add a little more flour until slight ball starts to form.
Cover and refrigerate dough at least 2-3 hours or up to a few days.
Preheat oven to 350 degrees F. Prepare baking sheet and spray with cooking spray or parchment paper.
Using a cookie scoop, scoop about 1½ tablespoon cookie dough. Roll cookie dough between hands to get a nice round ball and place on prepared cookie sheet.
Bake for 8-15 minutes.
TIP: This recipe is incredibly popular and has been made by thousands. While this recipe works for 90 percent of readers, another 10% it appears raw. If the cookies appear raw after baking and undercooked, continue to cook an extra 5-15 minutes. Every oven is different so use your best judgment on this recipe.
Removed from oven and while still hot, slightly press down if desired.
Allow cookies to cool down completely before transferring. Cookies will slightly harden overnight a little more so don't bake them much longer.
To make the glaze, combine powdered sugar and water together in a small bowl. Whisk fast until ingredients are combined with no lumps.
Dip cookies upside down into icing or drizzle icing over the top and allow to harden.