Instructions:
Make the Dough: In a large mixing bowl, combine the warm water, granulated sugar, and salt. Sprinkle the active dry yeast on top and let it sit for about 5 minutes, until it becomes frothy. Add the flour and melted butter to the yeast mixture and mix until well combined. Knead the dough on a floured surface for about 5-7 minutes, until it is smooth and elastic. Place the dough in a lightly oiled bowl, cover with a damp cloth, and let it rise in a warm place for about 1 hour, or until doubled in size.

Preheat Oven: Preheat your oven to 450°F (230°C). Line two baking sheets with parchment paper and lightly grease them.

Prepare the Boiling Solution: In a large pot, bring the 10 cups of water and the baking soda to a rolling boil.

Shape and Stuff the Pretzels: Punch down the risen dough and divide it into 8 equal pieces. Roll each piece into a long rope, about 18 inches long. Flatten each rope slightly and sprinkle the shredded cheese along the center. Fold the dough over the cheese and pinch the edges to seal. Shape each stuffed rope into a pretzel by forming a U-shape, then crossing the ends over each other and pressing them onto the bottom of the U.

Boil the Pretzels: Gently place the pretzels, one at a time, into the boiling water for about 30 seconds. Use a slotted spoon to remove the pretzels and place them on the prepared baking sheets.

Add Toppings: Brush the tops of the pretzels with the egg yolk and water mixture, then sprinkle with coarse sea salt.

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

Serve: Allow the pretzels to cool slightly before serving. Enjoy your delicious cheese-stuffed pretzels!