In a large bowl or stand mixer, combine warm water, yeast, and sugar. Let sit 5 minutes until foamy. Add flour, salt, and melted butter. Mix and knead for 6–8 minutes until the dough is smooth and elastic.
Cover the dough with a towel and let it rise in a warm place for about 1 hour or until doubled in size.
Preheat & Prep:
Preheat oven to 425°F (220°C). Line a baking sheet with parchment paper and lightly grease.
Shape the Pretzel Dogs:
Punch down the dough and divide into 8 equal pieces. Roll each piece into a long rope (about 18 inches), then wrap it around each hot dog, pinching the ends to seal.
Boil the Dough:
In a large pot, bring 10 cups water and baking soda to a boil. Carefully drop each wrapped hot dog into the boiling water for about 30 seconds. Use a slotted spoon to transfer them to the prepared baking sheet.
Egg Wash & Bake:
Brush each pretzel dog with beaten egg and sprinkle with coarse salt. Bake for 15–18 minutes, or until deep golden brown.
Serve:
Let cool for a few minutes before serving. Enjoy with mustard, ketchup, or cheese sauce!