In a large mixing bowl, combine warm water, flour, sugar, yeast, and kosher salt.
Mix the dough with a dough hook or wooden spoon until fully combined.
If using a dough hook, mix until a ball forms. If using a spoon, knead the dough until it becomes slightly sticky and forms a ball.
Transfer the dough to a greased bowl, cover it, and let it rise in a warm place for about an hour, or until it has doubled in size.
Divide the dough into 12 pieces and roll each piece into a thin rope.
Wrap each rope around a hot dog and place them on a parchment-lined tray.
In a large pot, combine 8 cups of water and baking soda. Bring to a boil, then reduce to a simmer.
Carefully add the pretzel-wrapped hot dogs to the simmering water in batches, boiling for 30 seconds each.
Using a slotted spoon, transfer the pretzel dogs to a parchment-lined baking tray. Preheat your oven to 425°F.
In a small bowl, whisk the egg with a splash of water. Brush the egg wash over the dough. Bake in the oven for 13-15 minutes, or until golden brown.
While baking, melt the butter. Once the pretzel dogs are browned, remove them from the oven, brush with melted butter, and sprinkle with coarse salt.