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To make the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. In a large bowl combine the flours, salt, and yeast. Stir in the beer, water, honey, and butter.
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Turn the rough dough onto a lightly oiled surface and knead it briefly, just enough to bring it together in a cohesive mass. You can also do this right in the mixing bowl, if you choose. The dough will be stiff, yet still sticky. That's OK; don't add any additional flour.
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Cover the bowl and place it somewhere warm. After 30 minutes, run a bowl scraper, spatula, or your fingers down the inside far wall of the bowl, bring the dough up from the bottom, and fold it over on top of itself. Repeat three times, rotating the bowl 90° each time.
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Cover the bowl and let the dough rest for an additional 30 minutes before refrigerating for 8 to 16 hours.
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Remove the dough from the refrigerator, and divide it into 10 pieces. (A bench knife is a helpful tool here.)
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Shape each piece into a smooth ball. Let the dough balls rest, uncovered, for 10 minutes.
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To shape pretzels: Form each dough ball into a 5" log.
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Roll the logs into 22" ropes, leaving a fatter portion in the center about 6" long.
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Twist each rope into a pretzel. Place the pretzels on a parchment-lined baking sheet. Don't crowd them; they're going to expand somewhat.
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Cover the pretzels and let them rest and rise at room temperature for 30 to 45 minutes.
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After the rest, chill the pretzels in the refrigerator for about 30 minutes or in the freezer for 15 minutes; this helps to firm them up and makes them easier to dip (though you can skip this step if you’re pressed for time). While the pretzels are chilling, make the cheese sauce.
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To make the cheese sauce: In a small saucepan set over medium heat, melt the butter, stir in the flour, and cook the mixture for about 30 seconds.
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Add the mustard or mustard powder and Worcestershire sauce.
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Slowly pour in the beer, whisking to incorporate. Once the sauce is smooth, remove the pan from the heat.
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Add the cream cheese, stirring to incorporate the pieces as they melt. Stir in the cheddar cheese. It won’t fully melt; that’s OK. Set the sauce aside to cool.
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Preheat the oven to 425°F.
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To finish and bake the pretzels: Prepare the water bath by combining the boiling water with the baking soda in a shallow dish or pan, stirring to dissolve the baking soda as best you can. Let cool until you’re ready to soak the pretzels.
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Place the pretzels into the water bath and allow them to soak for about 30 seconds. Remove the pretzels, letting the excess water drip off before placing them back on the baking sheet.
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Top the pretzels with coarse kosher or pretzel salt. Using a sharp knife or lame, slash each pretzel horizontally across its base.
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Bake the pretzels for 18 to 22 minutes, until deeply browned.
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To serve the pretzels: Rewarm the cheese sauce in the saucepan or microwave until hot; the cheddar cheese will melt, making a smooth sauce.
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Serve pretzels warm or at room temperature with the hot cheese sauce.
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Storage information: Store pretzels, well-wrapped, for up to 3 days at room temperature; freeze for longer storage.