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In a bowl (I used a stand mixer with a dough hook), combine the yeast with warm water. Stir and let sit for 5 minutes. The yeast should be bubbly.
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Add the 3 3/4 cups of bread flour, sugar, kosher salt, and butter to the water mixture. Knead the dough at medium speed until the flour is evenly moistened, 2 minutes. Increase the speed to high and knead until a smooth, elastic dough forms around the hook, 8 minutes. You can add more flour and water as needed.
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Transfer the dough to a lightly floured surface. Cover loosely with a dry kitchen towel and let rest for 5 minutes. Cut the dough into 8 equal pieces and form each one into a ball. Cover the dough balls with the towel and let rest for another 5 minutes.
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On an un-floured surface, roll each ball of dough into an 18-inch-long rope, tapering them slightly at both ends. To shape each pretzel, form the rope into a U shape. Cross the ends over each other twice to form the twist, then bring the ends to the bottom of the U and press the tips onto it.
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Arrange the pretzels on 2 large baking sheets lined with parchment paper and let stand uncovered in a warm place for 45 minutes, or until slightly risen.
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Refrigerate the pretzels uncovered for at least 2 hours or overnight.
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Preheat the oven to 400°.
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Heat 1/2 cup of baking soda in a large pot of water, bringing it to a boil.
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Using a slotted spatula, gently lower a pretzel into the solution for 30 seconds on each side. With the spatula, remove the pretzel and return it to the baking sheets.
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Brush the pretzels with the egg wash and then sprinkle with coarse salt and bake on the top and middle racks of the oven until shiny-brown and risen about 13-17 minutes; shift the pans halfway through baking.
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Let the pretzels cool slightly on the baking sheets before serving.