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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.
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Allow to sit for about 10 minutes or until the mixture begins to foam.
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Add flour and butter.
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Using the dough hook attachment, mix on low speed until well combined.
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Increase speed to medium. Knead until the dough is smooth and pulls away from the side of the bowl, 4 to 5 minutes.
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Remove the dough from the bowl, clean the bowl and then oil it well with vegetable oil.
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Return the dough to the bowl, cover with plastic wrap and sit in a warm place for 50 to 55 minutes or until the dough has doubled in size.
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Preheat the oven to 450° F.
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Line 2 half-sheet pans with parchment paper and lightly brush with the vegetable oil. Set aside.
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Bring the 10 cups of water and the baking soda to a rolling boil in an 8-quart pot or saucepan.
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While oven heats and water comes to boil, turn the dough out onto a slightly oiled work surface and divide into 10 equal pieces.
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Roll out each piece of dough into a 24-inch rope.
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Wrap dough around each hot dog in a circular fashion.
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Tuck both ends under wrapped dough.
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Place onto the parchment-lined half sheet pan.
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Place pretzels dogs into the boiling water, 1-2 at a time, for 30 seconds.
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Remove them from the water using a large flat spatula.
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Return to the half sheet pan, brush the top of each pretzel with the beaten egg yolk and water mixture and sprinkle with the pretzel salt.
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Bake until dark golden brown in color, approximately 12 to 16 minutes.
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Transfer to a cooling rack for at least 5 minutes before serving.
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Serve with spicy mustard or ketchup.