Combine water, yeast, sugar, and salt in a stand mixer bowl. Let stand for 10 minutes until foamy.
Add rosemary, flour, and butter. Knead on medium speed for 12 minutes.
Cover dough with a damp cloth and let rise for 1 hour or until doubled in size.
Combine mozzarella and parmesan in a bowl and freeze until needed.
Preheat oven to 425°F. Line two baking sheets with parchment paper.
Bring water and baking soda to a boil in a large pot.
Divide dough into 8 equal rounds, roll each into a 16″ rope, and then flatten into a 4″ wide strip.
Place 2 tablespoons of cheese filling along each strip, roll tightly into a rope, and shape into pretzels.
Boil each pretzel for 30 seconds, then transfer to baking sheets.
Brush pretzels with egg wash and bake for 16-18 minutes.
Brush with melted butter and sprinkle with additional toppings if desired.