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Combine the warm water, sugar and kosher salt in the bowl of a stand mixer and sprinkle the yeast on top. Let the mixture sit for about 5 minutes, until the yeast is foamy and begins to smell of yeast.
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Add the flour and butter to the yeast mixture. Attach the dough hook to the stand mixer and, on medium-low speed, combine the mixture until the dough pulls away from the sides of the bowl and appears shiny, roughly 4 to 5 minutes.
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Spray a large bowl with non-stick spray (or lightly grease with vegetable oil) and place dough in greased bowl. Cover with plastic wrap. Place bowl in a warm area and let dough rise for about 1 hour, or until doubled in size.
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Preheat oven to 450 degrees. Line two cookie sheets with parchment paper. Spray parchment paper with non-stick spray. Set aside.
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In a large pot, bring the 10 cups of water and the baking soda to a roiling boil.
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Place the dough on a greased surface, and divide into 16 equal pieces. Roll each piece into a long rope, roughly 12 inches long. Carefully wrap each piece around a half hot dog. Pinch the ends together to seal the dough.
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Boil the shaped pretzels and pretzel dogs, one at a time, in the baking soda water for 30 seconds each. Using a slotted spatula, remove each pretzel dog from the water and place it on a drying rack to allow any extra baking soda mixture to drip off.
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Place the boiled pretzel dogs back on a parchment lined baking sheets.
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Brush with beaten egg yolk and sprinkle with pretzel or kosher salt.
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Bake until golden brown, roughly 14 to 15 minutes. Transfer pretzel dogs to a cooling rack for a few minutes before serving. Serve with a variety of mustards.