In a large stand mixer with a dough hook attachment, combine warm water, yeast, sugar and salt. Let the mix stand for 10-15 minutes or until the yeast starts to foam
Add in flour and butter, and knead on medium for 10 minutes or until the dough is smooth and shiny
Cover the bowl with a damp towel and store in a warm place for one hour or until the dough has doubled in size.
Preheat the oven to 425°. In a small bowl, combine mozzarella and parmesan.
On the stove, fill a large pot with water and baking soda and bring to a boil.
While the water heats, assemble the pretzels: divide the dough into 8 equal parts
On a floured surface, roll each dough ball into a rope, 1- 1⅓ feet long.
Use a rolling pin to flatten the rope out into a rectangle. Fill the center of each rectangle with 2 tbsp of the cheese mixture and tightly roll/pinch the dough back together around the cheese.
Take both ends of the rope and make a U shape, then cross the ends down over each other and pinch onto the bottom of the "U"
Using a slotted spoon, carefully drop each pretzel into the boiling water for 30 seconds, immediately transferring to a baking sheet lined with parchment paper.
After all pretzels have been dipped in the water, beat together the egg and water and brush the tops of each pretzel
Bake for 15-17 minutes or until the pretzels are a deep brown color all over.