Buttery lemon shortbread cookies with a tart and sweet lemon icing are delightful with a cup of tea and for a light sweet snack. They are so tender and slightly crisp, and the icing just melts in your mouth. I love to serve these on a cookie platter during the holidays, but also they're wonderful any time of the year!
Make the cookie dough. Combine soft butter, sugar and lemon zest in a large bowl and cream together until pale and fluffy, scraping down the sides of the bowl as needed. Next, add the lemon juice and vanilla and mix again. Finally, add the flour and salt and mix until just combined. Turn the dough out onto a floured surface and flatten into a disk. Wrap the dough and chill for 15 to 30 minutes until firm but still pliable.
Lightly sprinkle flour over a work surface. Roll the dough out to about ¼ inch thick. You can also roll the dough between two pieces of parchment paper. Use a 2” round or scalloped cookie cutter to cut out desired shapes. Transfer cut-outs to the prepared baking sheets spacing them 2 inches apart and bake for 14-16 minutes until the edges are just lightly golden and the bottoms are golden. Keep any extra cut-out cookies in the fridge until ready to bake.
Remove from the oven and transfer the cookies to a wire rack to cool.
Make the icing. Combine powdered sugar, lemon juice and milk in a medium bowl and whisk until smooth. It should be quite thick and opaque so that it sets hard on the cookies once dry. If you think it is too thick to spread, you can add a tiny bit more lemon juice or milk until it reaches the desired consistency.
Spoon the icing over the cookies and spread it out a bit, but not all the way to the edges (leave a small border). Finely grate some lemon zest over the icing while icing is still wet, then let cookies set until the icing is hardened before storing in an airtight container.