01 - In a large mixing bowl, combine the warm water, active dry yeast, and granulated sugar. Allow the mixture to rest for 5 minutes, or until a foamy layer forms on the surface.
02 - Add the all-purpose flour, salt, and melted unsalted butter to the yeast mixture. Mix thoroughly until a cohesive dough forms, then transfer to a clean surface and knead for 5 to 7 minutes until the dough becomes smooth and elastic.
03 - Place the kneaded dough in a lightly greased bowl, cover it, and let it rise in a warm, draft-free location for 45 to 60 minutes, or until its volume has doubled.
04 - While the dough is rising, preheat your oven to 450°F. Line two large baking sheets with parchment paper.
05 - In a large pot, bring 10 cups of water and the baking soda to a rolling boil.
06 - 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 twist and shape it into a traditional pretzel form.
07 - Carefully immerse each shaped pretzel into the boiling baking soda solution for 30 seconds. Using a slotted spatula, remove the pretzel and place it onto the prepared parchment-lined baking sheets.
08 - Brush the surface of each pretzel generously with the egg wash and then sprinkle with coarse sea salt.
09 - Bake the pretzels for 12 to 14 minutes, or until they achieve a deep golden-brown color. Allow them to cool slightly on a wire rack.
10 - For the cheese sauce, melt the unsalted butter in a saucepan over medium heat. Whisk in the all-purpose flour and cook for 1 minute, creating a roux.
11 - Gradually whisk in the whole milk, ensuring no lumps form. Continue to cook, stirring constantly, until the sauce thickens, which typically takes about 2 to 3 minutes.
12 - Remove the saucepan from the heat. Stir in both the sharp cheddar and mozzarella cheeses, Dijon mustard, garlic powder, salt, and freshly ground black pepper until the sauce is smooth and all the cheese has melted.
13 - Serve the warm soft pretzels immediately with the prepared cheese sauce for dipping.