In a small bowl, combine warm water, sugar, and yeast. Let it sit for about 5 minutes until frothy.
In a large mixing bowl, combine flour and salt. Pour in the yeast mixture and melted butter. Mix until a dough forms.
Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic.
Place the dough in a greased bowl, cover with a towel, and let it rise in a warm place for about 1 hour or until doubled in size.
Preheat the oven to 425°F. Line a baking sheet with parchment paper.
Punch down the risen dough and divide it into 12 equal pieces.
Flatten each piece into a circle, place a cube of mozzarella in the center, and fold the dough over to seal it.
Roll each stuffed ball into a long rope and twist it into a pretzel shape.
In a large pot, bring 10 cups of water and baking soda to a boil.
Carefully drop each pretzel into the boiling water for about 30 seconds, then remove with a slotted spoon and place on the prepared baking sheet.
Brush each pretzel with the beaten egg and sprinkle with coarse sea salt.
Bake for 12-15 minutes or until golden brown. Allow to cool slightly before serving.