Combine warm water, active dry yeast, and granulated sugar in a small bowl. Stir gently and wait until the mixture becomes frothy.

Mix all-purpose flour and salt in a large bowl. Add the yeast mixture and stir until the dough forms.

Turn the dough onto a floured surface and knead until smooth and elastic. Place in a greased bowl, cover, and let it double in size.

Punch down the dough and divide it into equal pieces. Roll each piece into a rope long enough to wrap around a hot dog and cheese slice.

Wrap each cheese-covered hot dog with a dough rope and pinch to seal. Briefly boil each wrapped dog in water with dissolved baking soda, then place on prepared sheets.

Brush each pretzel dog with beaten egg and sprinkle coarse salt. Bake until golden brown, then cool slightly before serving with mustard or your choice of dip.