WHIRL flour, sugar and salt in a food processor. Add butter and pulse until mixture is coarse.
DRIZZLE in milk through feed tube with motor running until dough comes together.
KNEAD dough on work surface (without added flour) until a smooth ball forms. Flatten into a square and wrap in plastic wrap. Refrigerate for at least 1 hour.
PREHEAT oven to 350F. Line 2 baking sheets with parchment.
ROLL dough on lightly floured surface to a scant ¼-in.-thick square. Cut out using crinkled square 2-in. cookie cutter, rerolling scraps. Arrange on prepared baking sheets.
BEAT egg yolk with a few drops of water and brush each cookie. Drag tines of fork across cookie in a cross-hatch pattern. Chill for 10 min.
BAKE until dark golden and crisp, 15 to 18 min. Transfer to a rack to cool completely. Stir lemon zest, lemon juice and icing sugar until smooth. Brush over cookies. Cookies will keep well in a covered container at room temperature for up to 1 week. Baking Tip: Make dough up to 2 days ahead. Glaze cookies on the day of serving. Glazing too far ahead of time may create a crystallized pattern.