In a large mixing bowl, whisk together the water, sourdough discard, and sugar until dissolved. Add the flour, butter, and kosher salt and mix until a cohesive dough forms.
1 ¼ cups (300 grams) warm water, ½ cup (113 grams) sourdough starter discard, 1 tablespoon (12 grams) granulated sugar, 4 ¾ cups (565 grams) all-purpose flour, 4 tablespoons (57 grams) unsalted butter, 1 tablespoon (12 grams) kosher salt
Turn the dough out onto a lightly floured surface and knead for 8-10 minutes or until smooth and elastic.
Return the kneaded dough to the mixing bowl and let it rise in a warm place (about 75°F) for 4 hours or until it doubles in size.
Once the dough has risen, turn it out onto a lightly floured surface. Divide it into 8 equal pieces (about 130 grams each). Roll each piece into a 24-inch rope. Form each rope into a pretzel by making a U-shape, twisting the ends around each other, and pressing them onto the bottom of the U.
Place the shaped pretzels onto a baking sheet lined with parchment paper. Cover and let proof for 1 hour.
Preheat the oven to 450°F. Prepare a water bath by bringing 10 cups of water and ⅔ cup of baking soda to a boil in a large, shallow saucepan.
10 cups water, ⅔ cup baking soda
Once the water bath is boiling, carefully place each pretzel into the water, one at a time, for about 30 seconds each. Use a large spatula to transfer the boiled pretzels back to the baking sheet.
In a small bowl, whisk together the egg yolk and water to make an egg wash. Brush the pretzels with the egg wash and sprinkle them generously with coarse salt.
1 large egg yolk + 1 tablespoon water
Bake the pretzels for 12-15 minutes or until they develop a dark brown crust.
Allow the pretzels to cool for 10 minutes before serving warm with mustard, cheese sauce, or melted butter. Enjoy!