Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large mixing bowl, cream together the softened butter and 1/2 cup of powdered sugar until light and fluffy.
Add the lemon zest and lemon juice to the butter mixture, mixing until well combined.
In a separate bowl, whisk together the flour, salt, and baking powder.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Using a small cookie scoop or tablespoon, drop rounded balls of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake in the preheated oven for 12-15 minutes, or until the edges are lightly golden. The centers may look slightly underbaked, which is perfect for meltaway cookies.
Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
Once cooled, dust the cookies with the remaining powdered sugar before serving.