In a large bowl, mix warm water, sugar, and yeast. Let sit for 5 minutes until foamy. If not, start over with fresh yeast.
Add flour, salt, and melted butter. Stir to combine, then knead by hand or with a mixer for 5 minutes until smooth. Add flour 1 tablespoon at a time if sticky.
Place dough in a greased bowl, cover, and let rise in a warm spot for 1 hour, or until doubled in size.
Mix mozzarella, Parmesan, and chopped rosemary in a bowl.
Punch down dough and divide into 12 pieces. Flatten into 4-inch circles. Add 2 tablespoons of filling to 6 circles, top with remaining dough, and seal edges well.
Preheat oven to 450°F. Boil 10 cups of water, remove from heat, and slowly stir in baking soda. Dip each pretzel for 30 seconds, then place on a parchment-lined sheet.
Brush with egg, sprinkle with sea salt and rosemary. Bake for 12–15 minutes, until golden and cheese is bubbling.