Preheat the oven to 350° F (180°C). Line a cookie sheet with parchment paper and set aside.
In the bowl of a stand mixer or with an electric hand mixer, combine the butter, powdered sugar and egg until smooth and creamy.
1 cup (222g) salted butter, softened , 1 1/4 cup (137g) powdered sugar, 1 egg
Add the lemon oil and lemon zest, mixing until evenly distributed.
1 tsp lemon oil, 1 tbsp lemon zest
Add the cake flour, baking powder and salt. Mix until a sticky dough forms. Allow the dough to rest for 5 or so minutes- it will be easier to handle that way.
2 1/2 cups (295g) cake flour, 1/2 tsp salt , 1 tsp baking powder
Portion out the dough into small, 1/2 tbsp portions. Roll into a ball and arrange on the cookie sheet. Repeat with remaining dough.
Bake at 350° F (180°C) for 7-9 minutes, or until the cookies have spread slightly and look dry on the top.
While the cookies are baking, make the icing by combining the butter and vegetable shortening until smooth.
2 tbsp salted butter, 1/2 tbsp vegetable shortening
Add the powdered sugar and enough lemon juice to bring the mixture together into a thick frosting.
3/4 cup (80g) powdered sugar, 1/2 lemon juiced
Continue mixing while adding the rest of the lemon juice to thin out the icing.
As soon as the cookies come out of the oven, dip, spread or brush the icing onto the cookie and garnish with a little extra lemon zest, if desired.
Allow the cookies to cool and enjoy!