Cream butter and sugar until light and fluffy. Beat in 2 egg yolks and vanilla. Gradually beat in flour and salt. Divide dough into two portions; shape each into a disk. Cover; refrigerate until firm enough to roll, about 30 minutes.
Preheat oven to 350°. Working with one portion of dough at a time, roll to 1/4-in. thickness between parchment. Cut with floured 2-in. round cookie cutter. Place 1 in. apart on ungreased baking sheets. Whisk remaining egg yolk and water; brush over cookies. Create a cross-hatch design by dragging the tines of a fork across the cookie.
Bake until edges are light golden, 12-15 minutes. Cool on pan for 5 minutes. Remove to wire racks to cool completely.
