In a mixing bowl, combine the warm water, yeast, and sugar. Let it sit for about 5 minutes until it becomes foamy.
In a separate bowl, whisk together the flour and salt. Gradually add the flour mixture to the yeast mixture, stirring until combined.
If using a stand mixer, knead the dough with the dough hook for about 5 minutes until the dough is smooth and elastic. If mixing by hand, turn the dough out onto a floured surface and knead for about 8 minutes.
Incorporate the chopped rosemary and grated Parmesan into the dough. Form the dough into a ball and place it in a greased bowl, covering it with a towel. Let it rise for about 1 hour, or until doubled in size.
Preheat your oven to 425°F (220°C) and line a baking sheet with parchment paper.
Once the dough has risen, punch it down and divide it into 8 equal pieces. Flatten each piece and place a cube of mozzarella in the center. Fold the dough around the cheese to seal, forming a ball.
Roll each ball into a rope about 24 inches long, then twist it into the shape of a pretzel and place it on the prepared baking sheet.
In a saucepan, bring 4 cups of water to a boil. Add the baking soda carefully. Using a slotted spoon, drop each pretzel into the boiling water, cooking for about 30 seconds each. Remove and let them drain on paper towels.
Brush each pretzel with melted butter, then sprinkle with coarse sea salt.
Bake in the preheated oven for 12-15 minutes or until golden brown.