Activate the yeast: Whisk together the milk, sugar and yeast. Cover with plastic wrap and let the yeast activate for 15 minutes or until foamy and fragrant.
Make the dough: Stir the sourdough discard into the yeast mixture until completely incorporated.
In the bowl of a stand mixer fitted with the dough hook attachment, add the dry ingredients: the bread flour and salt. Then, add in the yeast mixture and the butter. Knead the butter into the dough until fully absorbed and there are no bits of flour.
Strengthen the dough: Continue to knead for 5 minutes in your mixer. (If you're not using a mixer, turn the dough out onto a clean surface and knead for 5 to 10 minutes, or until it feels smooth and elastic.) Building a strong gluten network is essential for pretzels, so take the time to ensure the dough is well-developed before proceeding.
Return the dough to the bowl and cover with plastic wrap.
Prep the hot dogs: Blot the hot dogs with paper towels, and try to get as much moisture off them as possible. Too much moisture will make the pretzels soggy and gummy.
Shape the pretzel dogs: Flatten the dough out into an 8-inch square. Divide the dough into 6 even strips. Roll each portion of dough into a 12-inch rope.
Starting at one end, wrap the dough tightly around the hot dog, tuck the ends in and pinch the dough so it doesn’t unravel. Repeat until all of the hot dogs are wrapped.
Transfer the pretzel dogs to a parchment-lined baking sheet. Freeze the tray uncovered while the oven heats up.
Preheat the oven to 425°F.
Baking soda bath: When the oven is ready, whisk the baking soda into the hot water until dissolved. Drop 1 pretzel dog into the baking soda bath for 1 minute, and transfer to a wire rack to drain. Repeat with the remaining pretzel dogs.
Sprinkle the pretzel salt on top of the dough. Return the pretzel dogs to the lined baking sheet. Bake for 15 to 20 minutes or until evenly browned.
Brush the top of each bun of the pretzel dogs with melted butter and serve.
The pretzel dogs are best enjoyed the day they are baked but will store well in an airtight container in the refrigerator for up to 3 days.