Preheat the oven to 350°F.
Add sugar and lemon zest to the stand mixer bowl and whisk together releasing the lemon essential oil.
Add softened butter and beat with the paddle attachment until light and fluffy.
Add the egg, and vanilla extract to the sugar mixture and beat until smooth.
Sift flour, and baking powder into a small mixing bowl. Stir in the kosher salt. Add the flour mixture to the stand mixer bowl and stir until just combined.
Portion the dough with a medium cookie scoop and roll into balls. If the dough is too soft and sticky at this point, refrigerate it for about 10 minutes, and then roll into balls.
Add granulated sugar into a small bowl if using. Roll the cookie dough balls in granulated sugar. Place them on a lined baking sheet about 2” apart.
Baked for 11 minutes until the bottom edges are golden brown. Remove from the oven and allow the cookies to cool on the baking sheet for 5-10 minutes before moving them to a wire rack to cool completely.
To make lemon icing, add lemon juice, powdered sugar, salt and lemon zest into a small bowl. Mix with a whisk until smooth.
Dip the completely cool lemon cookies into the icing, allow the excess to run off back into the bowl. Place the dipped cookies onto a wire rack and allow the icing to solidify.