1. In the bowl of a stand mixer fitted with the paddle attachment, or by hand in a bowl with a sturdy silicone spatula, cream the butter and salt together on low speed until smooth, about 30 seconds.
2. In a separate bowl, whisk the egg yolks, gradually adding the sugar while whisking, until the yolks are light and fluffy – about a minute. With the mixer on low, add the egg yolks to the butter, stopping the mixer to scrape down any butter clinging to the sides so it all gets incorporated.
3. Sift together the flour and baking powder in a small bowl, then stir that into the creamed butter mixture until it’s completely incorporated. (Don’t overmix it.)
4. Pat the dough into a rectangle about 1-inch (3cm) thick, wrap in plastic, and chill for an hour. (The dough can be made up to five days in advance, and stored in the refrigerator.)
5. Line two baking sheets with parchment paper. Have a pastry scrape or thin metal spatula handy.
6. Cut the rectangle of dough in half and place one piece between two large sheets of parchment paper. Roll the dough until it is between 1/3- to 1/2-inch (1,25cm) thick. Peel off the top piece of parchment paper and, using a 2-inch (5cm) round cookie cutter, cut out circles of dough, place them on the prepared baking sheet at least 1/2-inch (2cm) apart. You may need to coax them off the parchment with the pastry scraper or spatula.
7. Roll the second piece of dough, cut out circles, and put them on the other baking sheet. (Scraps can be gathered up and rerolled to make additional cookies.) Chill the baking sheets of cookies in the refrigerator or freezer until firm.
8. To bake the cookies, preheat the oven to 350ºF (180ºC). Adjust the oven rack to the middle of the oven.
9. Beat the egg in a small bowl with the teaspoon of water. Remove one sheet of cookies from the refrigerator or freezer. Brush the tops of the cookies with the egg wash then use a fork to cross hatch a pattern on the tops of the cookies. Bake the cookies until the tops are golden brown, about 15 minutes, rotating the baking sheet in the oven midway during baking.
10. Remove the cookies from the oven and let cool on a wire rack. Brush the second baking sheet of cookies with the egg wash, rake a pattern across the tops with a fork, and bake them.