Prepare the Dough:

In a large mixing bowl, combine the warm water, sugar, and kosher salt. Sprinkle the yeast on top and let it sit for 5 minutes, until it starts to foam.

Add the flour and melted butter to the yeast mixture. Mix until the dough comes together and is smooth and elastic, about 4-5 minutes by hand or with a dough hook in a stand mixer.

Transfer the dough to a lightly oiled bowl, cover, and let it rise in a warm place for about 1 hour, or until doubled in size.

Prepare the Cheese:

While the dough is rising, cut the mozzarella string cheese in half. If using shredded mozzarella, roll it into small logs and freeze them for about 15 minutes to firm up.

Shape the Pretzels:

Preheat your oven to 450°F (232°C). Line a baking sheet with parchment paper or a silicone baking mat.

Turn the risen dough out onto a lightly floured surface and divide it into 12 equal pieces.

Roll each piece into a long rope, about 12-15 inches long.

Flatten the rope and place a piece of mozzarella cheese in the center. Enclose the cheese by pinching the dough around it, then gently roll the dough again to seal the cheese inside.

Shape the dough into a traditional pretzel shape by forming a U, crossing the ends over each other, and pressing them down onto the bottom of the U.

Prepare the Baking Soda Bath:

In a large saucepan, bring the 10 cups of water and the baking soda to a rolling boil.

Boil each pretzel (one at a time) in the baking soda water for 30 seconds, then remove with a slotted spoon and place on the prepared baking sheet.

Add the Topping:

Brush each boiled pretzel with the egg wash and sprinkle with coarse sea salt.

Bake the Pretzels:

Bake in the preheated oven for 12-15 minutes, or until the pretzels are golden brown.

Serve:

Allow the pretzels to cool slightly on a wire rack before serving. Enjoy them warm with your favorite dipping sauces, such as marinara sauce or garlic butter.