In the bowl of a stand mixer fitted with a paddle attachment (or with a medium bowl and a handheld electric mixer), beat the butter and sugar on medium-high speed until light and fluffy, about 3 minutes.
Beat in 2 egg yolks, then turn the speed to low and gradually mix in the flour until incorporated.
Wrap the dough in cling wrap and refrigerate until chilled, about 1 hour or up to 2 days.
When ready to bake, preheat the oven to 375°F (190°C) and line 2 baking sheets with parchment paper. Set aside.
On a floured surface, roll the dough out to ¼-inch (6-mm) thick and cut cookies using a 2-inch (5-cm) round cutter.
Place the cookies on the prepared baking sheets and, with a thin, sharp knife, score the tops to create a crosshatch pattern.
Whisk the remaining egg yolk with a few drops of water (up to ½ teaspoon) to loosen it, then brush it over the tops of the cookies.
Bake for 12-15 minutes, until golden. Let cool on wire racks, then store in an airtight container for up to 5 days.
For longer storage, freeze for up to 2 months. Defrost at room temperature for about an hour.