01 - Dissolve sugar in warm water in a large bowl. Sprinkle yeast over the surface and let stand for 5 minutes until foamy.
02 - Add melted butter and salt to yeast mixture. Gradually incorporate flour, mixing until shaggy dough forms. Knead on lightly floured surface for 5–7 minutes until smooth and elastic, or use stand mixer with dough hook.
03 - Place dough in greased bowl, cover, and let rise in warm location for approximately 1 hour until doubled in size.
04 - Preheat oven to 450°F and line two baking sheets with parchment paper.
05 - Divide dough into 8 equal pieces. Roll each into 18-inch rope, flatten slightly, and place mozzarella stick in center. Pinch edges tightly to seal cheese completely. Shape into classic pretzel form, ensuring no cheese is exposed.
06 - Bring 8 cups water and baking soda to boil in large saucepan, then reduce to simmer.
07 - Gently dip each pretzel into baking soda bath for 30 seconds. Remove with slotted spatula and transfer to prepared baking sheets.
08 - Brush each pretzel with beaten egg and sprinkle generously with coarse salt.
09 - Bake for 12–15 minutes until deep golden brown. While hot, brush with melted butter for extra flavor if desired. Serve warm.