Prepare the Dough:
In a stand mixer bowl, combine warm water, yeast, sugar, and salt. Let sit for 10 minutes until foamy. Add chopped rosemary, flour, and softened butter. Mix until a dough forms, then knead for 5–7 minutes until smooth.

Let the Dough Rise:
Place the dough in a lightly oiled bowl, cover with a clean kitchen towel, and let it rise for 1 hour, or until doubled in size.

Shape the Pretzels:
Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper. Punch down the dough and divide it into 8 equal pieces. Roll each piece into a rope, about 10–12 inches long. Place a tablespoon of shredded mozzarella in the center of each rope, fold the dough over the cheese, and pinch the edges to seal. Shape each piece into a pretzel by forming a U, twisting the ends, and bringing them over to form the pretzel shape.

Boil the Pretzels:
In a large pot, bring 10 cups of water and the baking soda to a boil. Carefully dip each pretzel into the boiling water for about 30 seconds, then remove with a slotted spoon and place on the prepared baking sheet.

Apply the Egg Wash:
Brush each pretzel with the beaten egg wash.

Add Toppings:
Sprinkle each pretzel with grated Parmesan cheese, chopped rosemary, garlic powder, black pepper, and a pinch of salt.

Bake the Pretzels:
Bake in the preheated oven for 12–15 minutes, or until golden brown.

Finish and Serve:
Remove from the oven and, if desired, brush with melted butter. Serve warm.