1 1/2 cups warm water (110 to 115 degrees), plus 12 cups water, for boiling
2 tablespoons sugar
2 teaspoons kosher salt
2 1/4 teaspoons (1 packet) active dry yeast
4 1/2 cups all-purpose flour
6 tablespoons unsalted butter, melted
2/3 cup baking soda
2 large egg yolks, beaten
Pretzel salt or additional coarse kosher salt, for finishing
In the bowl of a stand mixer fitted with the bread hook attachment, mix the 1 1/2 cups of warm water with the sugar and kosher salt on medium speed until the sugar has dissolved. Evenly sprinkle the yeast over the top and let sit until frothy, about 5 minutes. Add the flour and butter and mix on low speed until combined. Increase the speed to medium and knead until the dough begins to come away cleanly from the sides of the bowl, about 5 minutes. Transfer the dough to a work surface, then clean the bowl of the mixer and lightly brush with vegetable oil. Return the dough to the bowl and cover with plastic wrap. Place the bowl in a warm space and let the dough rise until doubled in size, about 1 hour.
While the dough is proofing, heat the oven to 450 degrees. Line two baking sheets with parchment paper and lightly brush with oil. In a large pot or Dutch oven, bring the remaining 12 cups water and the baking soda to a boil over medium-high heat.
Once the dough has doubled in size, place on a lightly oiled work surface, such as a plastic cutting board, and divide into 8 equal pieces. Use your hands to roll each piece into a log about 2 feet long. Grab each end of the snake and form into a U-shape. Bring the ends across one another and push into the bottom of the U to form a pretzel shape. Place on the prepared baking sheet and repeat with remaining dough.
One at a time, boil the pretzels in the baking soda water for 30 seconds, flipping once halfway through. Using a slotted spoon, transfer to the prepared baking sheet, gently shaking off any excess water. Repeat with the remaining pretzels.
Brush the pretzels with the egg yolk and sprinkle with pretzel salt. Bake until dark golden brown, 12 to 15 minutes. Serve warm.