In the bowl of a stand mixer fitted with a dough blade or a large bowl, sprinkle yeast over warm water. Let sit for a minute before stirring to combine. Let sit until frothy, 5-10 minutes.
Stir in the flour, sugar, salt, and 1/4 cup butter until the dough comes together.
On a lightly floured surface, knead the dough until smooth and elastic. Place in a lightly oiled large bowl, cover, and let rise until doubled, about 1 hour.
Preheat oven to 425 degrees F. Line a large baking sheet with parchment or lightly grease.
Add 10 cups water and baking soda to a large pot and bring to a boil.
On a lightly oiled surface, divide the dough into 12 equal pieces. Roll each piece into a 24 inch 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.
Place prepared pretzel dogs in boiling water, 2 at a time, for 30 seconds. Remove with a slotted spatula to the prepared baking sheet. Brush the tops with melted butter and bake in preheated oven until golden brown, 12-15 minutes. 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.