In a stand mixer with the dough hook attachment, combine warm water, yeast, sugar, and salt. Let the mixture sit for about 10 minutes until it becomes foamy. Incorporate the flour, butter, and chopped rosemary, and knead on medium speed for 12 minutes. Cover the dough with a damp, warm cloth and leave it in a warm spot to rise for 1 hour or until it doubles in size.

In a small bowl, mix the shredded mozzarella and grated parmesan. Place the bowl in the freezer until needed.

Preheat your oven to 425°F and line two baking sheets with parchment paper. Meanwhile, in a large pot or Dutch oven, bring 10 cups of water and the baking soda to a boil.

Divide the risen dough into 8 equal portions. Roll each piece into a 16-inch rope, then flatten it to about 4 inches wide. Take the cheese filling from the freezer and distribute 2 tablespoons of the cheese along the center of each dough rope. Roll the dough back up tightly, jelly-roll style, and pinch the edges to seal the cheese inside.

Shape each filled dough rope into a "U", cross the ends over each other, and press them onto the bottom of the dough to form a pretzel shape.

Place each pretzel, one by one, into the boiling water for 30 seconds. Use a slotted spoon to remove the pretzels, allowing excess water to drip back into the pot before transferring them to the prepared baking sheets.

Brush the top of each pretzel with the egg wash. Bake in the preheated oven for 16 to 18 minutes or until golden brown.

Let the pretzels cool on the baking sheet for 5 minutes. Optionally, brush with melted butter and sprinkle with parmesan, rosemary, garlic powder, black pepper, and a pinch of salt.