Combine the water, sugar and salt in the bowl of a stand mixer. (Make sure water isn't hotter than 115° or it will kill your yeast.)
Sprinkle yeast on top of the water and let it sit for 5 minutes, or until it's getting foamy.
Add the flour and butter and mix on low with the dough hook until combined.
Increase to medium speed and knead until the dough is smooth and begins to pull away from the edges of the bowl. This was more than 6 minutes for me and my little non-Kitchenaid mixer. :)
Remove the dough from the bowl (it's sticky) and place in a greased bowl, covered with plastic wrap.
Let rise in a warm room for an hour, or until doubled in size. Mine rose for over 2 hours before I got back to it, and it was fine.
Preheat the oven to 450° and line a large cookie sheet or two smaller ones with parchment paper. Spray the paper with cooking spray.
Bring the water and baking soda to a boil.
Separate the dough into 8 equal parts and shape into 12" ropes with your hands. I dusted my hands with flour to keep it from getting too sticky.
Wrap one piece of dough around each hot dog, leaving a little sticking out of each end. Pinch the ends of the dough together so they stay put.
Drop the pretzel dogs into the boiling water one at a time for 30 seconds. Remove with slotted spoon, place on cookie sheet and brush with the egg yolk and water mixture.
Sprinkle with sea salt and place in the oven for 12-14 minutes, or until golden brown.
Let cool before serving with mustard or hot cheese dipping sauce. Yum!
Notes
Adapted from Alton Brown's recipe for Food Network