In a mixing bowl, combine warm water, yeast, and sugar. Let sit for about 5 minutes, or until the mixture becomes frothy.
Add the flour, salt, rosemary, and half of the Parmesan cheese to the yeast mixture. Mix until a dough forms.
Knead the dough on a lightly floured surface for about 5-7 minutes until smooth and elastic.
Place the dough in a greased bowl, cover with a damp towel, and let it rise in a warm place for about 20 minutes, or until doubled in size.
Preheat your oven to 450°F (230°C) and line a baking sheet with parchment paper.
In a pot, bring about 10 cups of water to a boil, then add the baking soda.
Once the dough has risen, punch it down and divide it into 12 equal pieces. Flatten each piece and place a mozzarella ball in the center. Fold the dough over the cheese and roll it into a ball.
Carefully place each pretzel bite into the boiling water for about 30 seconds. Use a slotted spoon to remove them and place them on the prepared baking sheet.
In a small bowl, beat the egg and brush it over each pretzel bite. Sprinkle with the remaining Parmesan cheese and coarse sea salt.
Bake for 12-15 minutes, or until golden brown.
Allow to cool for a few minutes before serving.