Step 1

Line a baking sheet with parchment; sprinkle evenly with sugar to cover. Set aside.

Step 2

In a liquid-measuring cup, combine milk and yeast. In the bowl of an electric mixer fitted with the paddle attachment, combine flour, salt, and vanilla. Beat in milk mixture on medium-high speed until thoroughly combined, about 2 minutes. With mixer running, add butter, 1 tablespoon at a time, making sure it is fully incorporated before adding the next one. Once all butter has been added, increase speed to high and beat 5 minutes. Turn out dough, wrap tightly in plastic, and refrigerate at least 2 hours and up to overnight.

Step 3

Preheat oven to 350 degrees. Generously sprinkle sugar on work surface. Place dough on sugared surface; sprinkle with sugar to cover. Top with a piece of parchment, then roll out dough 1/4 inch thick. Using a 3-inch oval cutter, cut out cookies. Transfer to prepared baking sheet, spaced 1 inch apart. Sprinkle with additional sugar. Bake until deeply golden all over, 15 to 18 minutes. Let cool on sheet 5 minutes, then transfer to a wire rack and let cool completely.