Combine flour, baking powder, baking soda and salt in a small mixing bowl. Whisk together to mix well.
Add 1 tablespoon of lemon zest to the sugar and use your fingers to rub them together. The sugar should turn a light yellow color.
Add the sugar, butter and cream cheese to the bowl of a stand mixer. Beat on medium speed for 3 minutes until creamy. Scrape down the sides of the bowl.
Add 2 tablespoons of lemon juice and mix for another 30 seconds.
Finally, add the dry ingredients and mix on low speed until just combined.
Remove the bowl from the mixer, cover with plastic wrap and refrigerate for one hour.
Once the chilling time has passed, preheat the oven to 350ºF/180ºC. Line two baking sheets with parchment paper.
Scoop the cookie dough into balls approximately 1 1⁄2 tablespoons in size. Place them on the baking sheet spaced 2 inches apart. Use your fingers to flatten them slightly into discs.
Bake in the preheated oven for 12-13 minutes or until the edges are just set. The cookies will still be quite soft when you remove them from the oven. Allow them to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Once the cookies are cooled, prepare the icing: combine the powdered sugar, remaining 1 tablespoon lemon zest and 3 tablespoons of lemon juice in a small bowl. Mix well until no dry ingredients remain.
Use a teaspoon to drop icing on top of the cookies and use the underside of the spoon to spread it around the top.
Allow the icing to dry completely before storing.