Place the lemon zest, lime zest, and orange zest in a small bowl. In a separate bowl, combine the lemon juice, lime juice, and orange juice. Set aside.

Whisk together the flour, baking powder, and salt in a medium bowl. Set aside.

Using an electric mixer on medium speed, beat the butter and granulated sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition. Then, mix in the vanilla extract.

Gradually add the flour mixture, alternating with the citrus juice mixture. 

Add the zests and fold in until well combined. The dough should be sticky but soft.

Drop the dough by tablespoon-size portions onto the prepared baking sheet, leaving about 2 inches between the cookies.

Bake the cookies, one pan at a time, for 10 to 12 minutes, or until the edges are lightly golden. 

Remove the cookies from the oven and let them cool on the baking sheet for a few minutes. Then press the tops with the bottom of a glass to flatten them while the cookies are still warm. Transfer them from the pans to a wire rack to cool completely.

In a small mixing bowl, whisk together the confectioners' sugar, lemon juice, lime juice, and orange juice until smooth and well combined.

Once the cookies have completely cooled, drizzle or dip the tops of the cookies in the glaze. If you like, top each cookie with a sprinkle of citrus zest. Allow the glaze to set for about 15 to 20 minutes before serving or storing the cookies.