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In the bowl of an electric stand mixer fitted with a hook attachment, combine warm water and sugar. Sprinkle yeast on top of the water and let sit for five minutes, until foamy.
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Add flour, salt, and melted butter to the yeast. Mix on low until well combined. Switch to medium speed and knead for four minutes.
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Remove the sticky dough ball from the mixer bowl and add to a greased bowl, sprinkle with flour, and cover loosely with a dish towel. Place in a warm area to rise for at least an hour, until doubled in size.
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Preheat oven to 425 degrees F.
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Combine water and baking soda in a large stock pot. Bring to a boil.
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Meanwhile, turn the dough out on to a slightly oiled surface. Press the dough into a 1 ½ inch thick circle. Cut into 12 even pieces, 6 if you are wrapping whole brats.
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Roll the dough wedge out from the center using your fingers to form a foot long snake-like shape. Wrap the dough around the brat, making sure to seal the ends tightly. Continue until all brats are wrapped.
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When the water is boiling, add a few pretzel brats into the water at a time. Boil each batch for thirty seconds and then remove with a large slotted spoon or folded spatula. Transfer to a parchment lined baking sheet drizzled with a bit of oil to ensure the boiled pretzel brats don’t stick.
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Once all pretzel brats are boiled, brush with egg wash and then sprinkle with salt and pepper.
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Bake pretzels for 15 minutes until deeply golden.
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Pretzel brats last four days in the refrigerator wrapped in foil. Reheat in the oven wrapped in foil at 350 degrees F for 10 – 12 minutes.