In a standing mixer bowl, whisk together the water (at a temperature between 100-110 degrees Fahrenheit), yeast and sugar. Cover with a kitchen towel and let sit until foamy, around 5-10 minutes.*
Add the dough hook onto your mixer, and then add the melted butter, salt and 2 cups of the flour to the yeast mixture. Beat the dough at a low speed (speed 1 or 2) for about one minute, until the dough starts to come together. At this point, it should be very wet. Scrape down the sides of the bowl if you need to.
Add 1/4 cup more of the flour to the dough and continue mixing at a low speed for 1-2 minutes. Your dough may look like it's a bit too dry, but let it keep mixing and it should come together. If your dough is still very wet and sticky, add the remaining 1/4 cup of the flour and beat at a low speed until it comes together. If your dough is a bit dry, add 1 teaspoon of warm water and continue beat at a low speed until it has fully come together. The temperature and humidity of your home will greatly affect how much flour you end up needing. Remove the dough from the mixing bowl and hand knead it for 2-3 minutes until totally smooth. The dough should be tacky, but not sticky. Put the dough back in the bowl and cover with a kitchen towel to proof for 30-40 minutes, until it's doubled in size.
While the dough is proving, I like to use this time to grate my cheese if I didn't buy pre-shredded.
Preheat the oven to 400 degrees Fahrenheit.
Once the dough has doubled in size, remove it from the bowl and cut it into four equal parts. Using a rolling pin, roll each ball of dough into a thin, oblong shape, around 1/8 - 1/4 inch thick. Then roll the dough lengthwise like a hot dog to form the stick shape. Once all four pretzel sticks have been formed, throw a kitchen towel over them for 10-15 minutes while you prepare the baking soda bath.
Boil your 9 cups of water and then add the 1/2 cup of baking soda and keep the water at a boil. Gently take the pretzel sticks and lower them into the water and let sit for 25-40 seconds. Then remove using two spatulas, spoons with holes or spiders. Then place onto your baking tray.**
Score each pretzel stick twice with a sharp knife. Take your two sausages and cut them in half, then take each half and cut it lengthwise. Place each quarter of the sausage into the scored sections of the pretzel and then top with the 1 cup of shredded or grated cheese.
Bake for 18-21 minutes, until cheese is melted and pretzel is browned.