In the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl if mixing by hand), stir together warm water, yeast, and brown sugar. If using active dry yeast, let yeast mixture stand for 5-10 minutes or until foamy.
Stir in 2 cups flour and salt.
Continue stirring in flour 1/2 cup at a time until dough comes together. Dough will still be a little sticky. If you touch the dough, it should pull with your finger but shouldn't come off on your finger.
Cover the dough with plastic wrap or a clean towel, and let it rise in a warm place for about 10 minutes.
While dough is resting, preheat oven to 425 F. Line baking sheets with parchment paper or silicone baking mats.
To prepare the water bath, stir together remaining 6 cups warm water and 6 tablespoons of baking soda in a medium bowl.
To prepare the egg wash, mix egg yolk and water together. Set aside.
Divide dough into 10 pieces.
Roll each piece of dough into a rope approximately twice as long as the hot dog.
Wrap dough around the hot dog, pressing the ends of the dough in to seal them.
Repeat with the remaining dough and hot dogs.
Submerge shaped pretzel in water bath, and then place it on prepared baking sheets.
Brush each pretzel with the egg wash, and sprinkle with a little kosher salt.
Bake for 10-15 minutes, or until golden brown.
Serve with mustard or other desired sauces for dipping.
Notes
Warm water: If you don't have a kitchen thermometer to test the water temperature, the water should feel like bath water. If the water is too hot, it can kill the yeast.
Yeast: An equal amount of active dry yeast can be used in place of the instant yeast.
Brown sugar: You can use granulated sugar, if you prefer.
Kosher salt: Another coarse salt (like sea salt) will work.
Hot dogs: I go into more detail about hot dogs above the recipe, but you can use any brand of standard hot dog that you like.