Preheat the oven to 350 degrees F (175 degrees C).

Sift or whisk flour, salt, and baking powder together in a bowl.

Place butter in a large mixing bowl and mix with a wooden spoon until very creamy. Add confectioners' sugar, lemon juice, and flour mixture; mix until well combined.

Roll dough out on a lightly floured surface to 1/4-inch thickness. Cut into rounds using a round cookie cutter. Transfer cookies to ungreased baking sheets.

Bake in the preheated oven until cookies are light brown on the bottom but still very light on top, about 10 minutes. Allow cookies to cool on the baking sheets for about 2 minutes before transferring to wire racks to cool completely.

Whisk melted butter and lemon juice together in a small bowl. Add lemon zest and whisk again. Whisk in confectioners' sugar 1 cup at a time. Add more lemon juice if necessary for a thin consistency.

Dip the top of each cookie in the glaze and transfer to a wire rack placed over waxed paper or parchment paper. Allow cookies to sit until glaze has set, about 2 hours.

Store cookies in an airtight container between layers of waxed paper.