Because who doesn't like pretzels? This is an emended recipe from an emended recipe. The original dates from an old "Cooks Illustrated" which explains the crazy hard-boiled egg yolk addition. Apparently it lends a certain flakiness to the end result. Who's to know? The end result is delicious, flakiness or no.
Yield: People are insisting these make 40+ cookies. Well, that's bullcrap. If you make cookies properly (as in, so that you're not making them for ants), you'll get about 15 from this recipe. But, hey, ants need cookies too.
1 large egg, hard-boiled and cooled
10 tablespoons (140 grams or 1 1/4 sticks) unsalted butter, softened
1/3 cup plus 1 tablespoon (80 grams) granulated sugar
1/4 teaspoon table salt
1 1/2 teaspoons vanilla extract (this is halved from the original)
1 cup (125 grams) unbleached all-purpose flour
1/2 cup (45 grams) rye flour (medium or white will work)
1 large egg white, lightly beaten with 1 teaspoon water
4 teaspoons turbinado or clear sanding sugar
Place butter, sugar and salt in the bowl of stand mixer fitted with paddle attachment. Crack egg and peel shell. Separate yolk from white; add white to your next sandwich or egg salad. Press yolk through fine-mesh strainer and into mixer bowl with other ingredients. Beat mixture on medium speed until light and fluffy, scraping down sides of bowl and beater with spatula as needed. Add vanilla, mix until combined. Add flours and mix at low speed until just combined. Using rubber spatula or your hands, reach into bowl and knead dough a few times into a cohesive mass.
Shape the dough into a sort of log shape and place on parchment paper. Wrap tightly and chill in the fridge for about 30 minutes (or longer. Legend has it that the dough only improves the longer it's rested).
Heat oven to 350 degrees. Line two baking sheets with parchment paper.
Slice 1/4-inch off the chilled log and roll slice into a ball in the palm of your hands; this softens the dough. On a counter, roll ball into a 6-inch rope. Pick up each end of rope and fold turn it into the center, pressing it into a pretzel shape. Transfer to baking sheet. Repeat with remaining dough, placing cookies one inch apart on prepared sheets.
Brush each pretzel cookie with egg white wash, then sprinkle with coarse sugar. Bake cookies until they have golden brown edges, about 13 to 15 minutes. Remove from oven but let firm up on baking sheet for 5 minutes before transferring cookies to cooling racks.
Do ahead: Cookies stored in an airtight container between sheets of waxed or parchment paper will keep for at least one week.