In the large bowl of a stand mixer fitted with the paddle attachment (or in a large bowl with an electric mixer), mix butter and powdered sugar on low speed until sugar is incorporated and butter turns pale, about 2 minutes. Scrape down sides of bowl. Add egg, vanilla, and salt and beat on medium speed until combined, about 1 minute. Using a flexible spatula, fold in flour until just combined, being careful not to overmix. Tightly wrap dough in plastic and refrigerate until very firm, about 1 hour.
Preheat oven to 350°. Line 2 baking sheets with parchment.
Divide dough in half and keep one half wrapped in refrigerator. On a floured work surface, using a standard rolling pin, roll dough to a 12"-by-9" rectangle. Lightly dust top of dough with flour. Using a springerle rolling pin or cookie stamp, stamp patterns into dough, outlining about 20 cookies. Trim around edges of patterns, separating dough into individual cookies, and arrange on one of the prepared baking sheets.
In a small bowl, lightly beat egg yolks with a fork. Brush raised edges and patterns with yolks. Bake until set but not taking on color, 10 to 12 minutes. Repeat with remaining dough. Let cool completely on baking sheets.