Begin by combining the warm water, yeast, sugar, and salt in the bowl of a stand mixer fitted with the dough hook attachment. Let the mixture rest for about 10 minutes until it becomes foamy, indicating that the yeast is active.
Add the chopped rosemary, flour, and softened butter. Knead the dough on medium speed for approximately 12 minutes until it becomes smooth, elastic, and slightly tacky.
Transfer the dough to a lightly greased bowl and cover it with a warm, damp towel. Allow it to rise in a warm place for about one hour or until doubled in size.
While the dough rises, combine the shredded mozzarella and grated Parmesan in a small bowl. Place the cheese mixture in the freezer to help it stay firm during assembly.
Preheat your oven to 425°F (220°C). Line two large baking sheets with parchment paper.
Bring the 10 cups of water and baking soda to a gentle boil in a large Dutch oven or stockpot.
Punch down the risen dough and divide it into eight equal portions.
Roll each portion into a rope approximately 16 inches long. Flatten each rope until it measures about 4 inches wide.
Remove the chilled cheese filling from the freezer. Spoon about 2 tablespoons of cheese evenly down the center of each flattened rope.
Carefully roll the dough back into a rope, enclosing the cheese completely. Pinch the seam tightly closed to prevent any cheese from leaking during baking.
Shape each rope into a classic pretzel by forming a U shape, crossing the ends, twisting them once, and pressing them onto the bottom of the pretzel.
Working one at a time, carefully lower each Mozzarella Stuffed Soft Pretzel into the boiling baking soda bath for 30 seconds. Remove with a slotted spoon and transfer to the prepared baking sheets.
Brush each pretzel with the egg wash to create a beautiful golden finish.
Bake for 16 to 18 minutes or until deeply golden brown.
Allow the pretzels to cool for about 5 minutes before serving.
For the optional topping, combine the Parmesan, rosemary, garlic powder, black pepper, and salt. Brush the warm pretzels with melted butter, then generously sprinkle with the topping mixture before serving.