In a large bowl, mix warm water, flour, sugar, yeast, and salt. Stir with a dough hook or spoon until combined.
If using a dough hook, mix until a ball forms. If using a spoon, knead by hand until smooth and slightly sticky.
Place dough in a greased bowl, cover, and let rise in a warm spot for about 1 hour (until doubled).
Divide into 12 pieces. Roll each piece into a long rope.
Wrap each rope around a hot dog and place on a parchment-lined tray.
In a pot, bring 8 cups water + baking soda to a boil, then reduce to a simmer.
Boil pretzel dogs in batches for 30 seconds. Remove with a slotted spoon and return to tray.
Preheat oven to 425°F. Brush dough with egg wash.
Bake 13–15 minutes, until golden brown.
Brush with melted butter and sprinkle with coarse salt.
Serve warm with cheese sauce or mustard.