01 - In a large bowl, combine 1 ½ cups warm water, 2 ¼ teaspoons active dry yeast, and 1 tablespoon granulated sugar. Allow the mixture to sit undisturbed for 5 minutes until it becomes foamy.
02 - Add 4 cups all-purpose flour, 1 teaspoon salt, and 2 tablespoons melted unsalted butter to the yeast mixture. Mix thoroughly until a cohesive dough forms.
03 - Transfer the dough to a clean, lightly floured surface and knead it for 5 to 7 minutes until it develops a smooth and elastic consistency.
04 - Place the kneaded dough in a lightly greased bowl, cover it with plastic wrap or a clean kitchen towel, and let it rise in a warm environment for 45 to 60 minutes, or until its volume has doubled.
05 - Preheat your oven to 450°F (230°C). Line two large baking sheets with parchment paper to prevent sticking.
06 - In a large pot, combine 10 cups of water and ⅔ cup of baking soda. Bring this solution to a rolling boil over high heat.
07 - Gently punch down the risen dough to release air. Divide the dough into 8 equal portions. Roll each portion into a rope approximately 20 inches long, then carefully shape each rope into a classic pretzel form.
08 - Using a slotted spatula, carefully immerse each shaped pretzel into the boiling baking soda solution for exactly 30 seconds. Remove the pretzels and place them onto the prepared baking sheets.
09 - Brush the surface of each pretzel with the prepared egg wash (1 large egg beaten with 1 tablespoon water) and sprinkle generously with coarse sea salt. Bake for 12 to 14 minutes, or until the pretzels achieve a deep golden brown color.
10 - Once baked, transfer the pretzels to a wire rack and allow them to cool slightly before serving.
11 - For the cheese sauce, melt 2 tablespoons unsalted butter in a medium saucepan over medium heat. Whisk in 2 tablespoons all-purpose flour and cook, stirring constantly, for 1 minute to create a roux.
12 - Gradually whisk in 1 cup whole milk. Continue to cook the mixture, stirring frequently, until it thickens to a desired consistency, typically within 2 to 3 minutes.
13 - Remove the saucepan from the heat. Stir in 1 cup shredded sharp cheddar cheese, ½ cup shredded mozzarella cheese, ½ teaspoon Dijon mustard, and ¼ teaspoon garlic powder until the cheeses are fully melted and the sauce is smooth. Season with salt and black pepper to taste.
14 - Serve the warm, freshly baked soft pretzels immediately with the creamy cheese sauce for dipping.