1 3/4 cups warm (110 to 115 degrees F) water
1 tablespoon sugar
2 teaspoons kosher salt
1 package active dry yeast
22 ounces all-purpose flour, approximately 4 1/2 cups
1 large whole egg yolk beaten with 1 tablespoon water
Vegetable oil, for pan
Combine the warm water, sugar and kosher salt in the bowl of a stand mixer and sprinkle the yeast on top. Allow to sit for 5 minutes or until the mixture begins to foam. Add the flour and, using the dough hook attachment, mix on low speed until well combined. Change to medium speed and knead until the dough is smooth and pulls away from the sides of the bowl, approximately 4 to 5 minutes. Remove the dough from the bowl, clean the bowl and then oil it well with vegetable oil. Return the dough to the bowl, cover with plastic wrap and sit in a warm place for approximately 50 to 55 minutes or until the dough has doubled in size.
Preheat the oven to 350 degrees F.
Line 4 half sheet pans with parchment paper and lightly brush with the vegetable oil. Set aside.
Place enough water into a large roasting pan to come 1/3 of the way up the sides of the pan and bring to a boil over high heat.
In the meantime, turn the dough out onto a slightly oiled work surface and divide into 1-ounce portions, approximately 36 pieces. Roll out each piece of dough into a 14 to15-inch long stick and place on the sheet pans, 1/4-inch apart. Cover the dough not being used with a slightly damp towel to help prevent drying out.
Gently place 6 to 8 pretzels at a time into the water for 30 seconds. Remove the pretzels back to the sheet pan, brush with the beaten egg yolk and water mixture and sprinkle with the pretzel salt. Bake until golden brown in color and hard, approximately 55 to 60 minutes. Transfer to a cooling rack for at least 20 minutes before serving. Store in an airtight container for up to 1 week.