In a large mixing bowl, combine warm water, yeast, and sugar. Let it sit for about 5 minutes until frothy.
Add flour and salt to the yeast mixture and stir until a dough forms. Knead the dough on a floured surface for about 5 minutes until smooth.
Place the dough in a greased bowl, cover with a damp cloth, and let it rise in a warm place for 1 hour or until doubled in size.
Preheat the oven to 425°F and line a baking sheet with parchment paper.
Once the dough has risen, punch it down and divide it into 12 equal pieces. Flatten each piece and place a mozzarella stick in the center. Fold the dough around the cheese and roll it into a ball.
In a large pot, bring 10 cups of water to a boil and add the baking soda. Carefully drop each pretzel ball into the boiling water for about 30 seconds, then remove and place on the prepared baking sheet.
Brush each pretzel with the beaten egg, sprinkle with coarse sea salt and chopped rosemary.
Bake for 12-15 minutes or until golden brown. Let cool slightly before serving.