Preheat the oven to 350°F, and line baking sheets with parchment paper.
In a large bowl, use an electric mixer to cream the butter and sugar together until very pale and fluffy (about 5 minutes). Stir in the egg and the yolk until completely incorporated (about 2 minutes).
Add the citrus zest, flour, cornstarch, baking soda, and salt, and stir together until just combined.
Use a 1½ tablespoon scoop to portion out the dough on the prepared cookie sheets.
Bake for 12 to 16 minutes, or until the cookies are just beginning to turn golden around the edges, but are still soft in the center.
Cool completely.
ADD THE ICING:
In a medium bowl, stir the powdered sugar, citrus juices, and citrus zests together until smooth. Then drizzle the icing over the cookies (it will be thin, so it's best to place the cookies on a rack set over a baking sheet so the icing can drip below).