• In a small bowl, sprinkle the yeast over 1 cup (237 milliliters) of the warm water. Stir to combine and let sit until frothy, about 10 minutes.
• In the bowl of a stand mixer fitted with a dough hook or a large bowl, combine the flour, sugar, and salt. Slowly mix in the yeast with water and butter. If needed, slowly add the remaining 1/4 cup (60 milliliters) water to create a soft dough.
• On a lightly floured surface, knead the dough until smooth and elastic. Transfer to a large bowl, cover with plastic or a towel, and allow to rise until doubled, 1-2 hours.

To assemble:

• Preheat oven to 425˚F (220˚C). Place the 8 cups (2 liters) water and baking soda in a pot and bring to a boil.
• Line two baking sheets with parchment or lightly grease.
• On a lightly oiled surface, divide the dough into 12 equal pieces.
• Roll each piece into a 24 inch (0.6 meter) long rope.
• Wrap the dough around the hot dog, pinching to seal the ends. As you wrap the dough around the hot dog, leave a large open spot on the upper third section for the head (remember the dough will expand as it bakes). Don’t stick to one direction, just try to make sure the ends are tucked into the underside of the hot dog. Repeat with remaining pieces.
• Reduce the heat to a low boil and gently place the dough-wrapped hot dogs into the water, being careful not to overcrowd. Turn to coat on all sides, boil for 30 seconds, and remove with a slotted spatula to the prepared baking sheet.
• In a small bowl, beat together the egg and 1 tablespoon (15 milliliters) water.
• Brush the top and sides of each boiled hot dog with the egg wash. Bake in the preheated oven until golden brown, 15-18 minutes.
• Immediately after removing from the oven, brush the tops and side of the golden pretzels with the melted butter.
• Let cool on a wire rack 5 minutes before making two eyes on each exposed area of hot dog with drops of mustard or sesame seeds.