Combine warm water, yeast, and sugar in a bowl. Stir and let sit about 5 minutes until foamy.

Mix flour and salt in a large bowl. Add yeast mixture and stir until a shaggy dough forms.

Knead dough on a floured surface for 5–7 minutes until smooth and elastic.

Place dough in an oiled bowl, cover, and let rise about 1 hour until doubled in size.

Preheat oven to 450°F. Line baking sheets and bring 10 cups of water to a boil. Stir in baking soda.

Punch down dough and divide into 8 pieces. Roll each into a 12–14 inch rope.

Wrap each hot dog with a slice of cheddar, then spiral dough around to fully cover.

Boil each wrapped pretzel dog in baking soda water for 30 seconds.

Transfer to baking sheets, brush with beaten egg, and sprinkle with coarse salt.

Bake for 12–15 minutes until deeply golden and glossy.

Cool for 3–5 minutes, then serve with mustard or dipping sauce.