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