BEAT butter and sugar in a large bowl with an electric mixer on medium, scraping sides and bottom of bowl, until fluffy, about 3 min. Beat in yolks, 1 at a time. Beat in salt and vanilla. Sift flour over butter mixture and beat on low until just combined.
KNEAD on work surface until smooth, about 10 times. Divide dough in half. Shape one half into a flat square on a piece of parchment. Roll out to a 9-in. square, dusting lightly with flour. Slide paper and dough onto a baking sheet, then repeat with remaining dough. Chill until firm, about 25 min.
PREHEAT oven to 325F. Line 2 baking sheets with parchment.
TRIM edges of dough to make a perfect square, then cut into 16 2-in. squares. Transfer to a prepared sheet.
BAKE until edges begin to brown, 14 to 16 min. Let cool for 3 min, then transfer to a rack to cool. Repeat with remaining dough.
ROYAL ICING: Beat egg whites and vinegar in a large bowl with an electric mixer on medium until foamy. Beat in sugar until combined, then increase speed to medium-high and beat until thick, 2 min. Beat in cold water to thin icing.
TRANSFER to a piping bag fitted with a very small plain tip. Pipe a border of icing around outer edges of cookie, then continue in concentric circles to the centre. Spread icing evenly with a skewer. Ice all cookies, then let sit at room temperature until icing hardens, about 8 hours.
STIR ½ tsp lustre dust and ½ tsp water in a small bowl, mixing with a paintbrush. Paint cookies as desired.
Nutrition (per cookie)
Kitchen Tip: Lustre dust is an edible powder used to add metallic sheen and colour. When mixed with water or clear alcohol like vodka, it can be used as a paint on royal icing or fondant. We found lustre dust at goldaskitchen.com. Metallic food paint would also work.