Add flour and butter to a bowl and mix until large crumbs form. Add sugar, salt, and lemon zest and stir to combine. Add egg and continue to mix until a smooth dough forms. Wrap dough in plastic foil and refrigerate for approx. 60 min.
Preheat oven to 180°C/350°F. Flour working surface and roll out dough until approx. 2-mm/0.1-in. thick. Use a cookie cutter to cut out cookies, then brush them with milk.
Transfer cookies to a parchment-lined baking sheet. Bake in the oven at 180°C/350°F for approx. 10 min. Let cool down on a cooling rack before serving. Enjoy!