First we're going to make the dough.
Add your warm water and sugar the bowl of a stand mixer stir to dissolve sugar. Sprinkle yeast across the top of the water and leave it for about 5 minutes. The yeast will start to foam.
Attach a dough hook to a stand mixer.
Add melted butter, salt and half of the flour to your mixing bowl. Mix on low speed until flour is incorporated (about 2-3 minutes) gradually add more flour until the dough begins to pull away from the sides of the bowl and isn’t as sticky. The exact amount of flour you will need will vary depending on how much moisture is in your flour, the environment etc. I usually use about 4 ½ cups of flour, just add it gradually and pay attention to your dough.
Turn up the speed to medium and allow to knead for about 5 minutes. If you prefer to knead by hand you can turn the dough out onto a lightly floured surface and knead until smooth.
Place the dough in a lightly greased bowl, cover loosely, set in a warm place and let rise for about an hour in or until doubled in size.
Once the dough has risen it is time to make the pretzel dogs.
Preheat the oven to 425 and line a baking sheet with parchment paper.
Place dough on a clean, lightly floured work surface. Divide dough into 15 equal pieces.
Take one of your pieces of dough and roll it into a long rope shape about 15 inches long.
Pat a hot dog dry with paper towels.
Starting at one end of the hot dog wrap the piece of dough around it and gently press. Continue wrapping the dough around the hot dog until it is completely wrapped. Gently press the end to secure it in place.
Repeat with the remaining hot dogs until all are covered with pretzel dough.
Place the 10 cups of water and ½ cup baking soda in a large stock pot on the stove and bring it to a boil.
Set your prepared baking sheet on the counter next to the stove.
Gently place a pretzel dog in the boiling water and cook for about 30 seconds. Using a slotted spatula or slotted spoon gently lift the pretzel out of the water and place the boiled pretzel dogs on the baking sheet.
Repeat with the remainder of the pretzel dogs. Placing them about 2 inches apart on the baking sheet. You may need to use 2 cookie sheets or work in batches.
Once they are all boiled it is time to bake them.
In a small bowl whisk together the egg and 1 tsp water until well mixed.
Using a brush coat the pretzels evenly with a thin coat of the egg mixture. Sprinkle on coarse salt as desired.
Place the baking sheet in the oven for about 15 minutes or until pretzels are a lovely deep golden brown.
Allow to cool until warm before serving. The inside is very hot right out of the oven.
Serve warm
Store refrigerated in an air tight container.