In a large bowl, combine your yeast and warm water. Stir together and let sit for 1 minute.
Add in the salt, brown sugar and melted butter, and stir together.
Add in the flour, 1 cup a time, until the dough is thick and no longer sticky. (Add in more flour 1 TBS at a time as needed if the dough is still sticky)
Lightly flour a flat surface.
Knead your dough for 3-4 minutes and form it into a ball.
Place the dough into a greased bowl and cover with a towel, and place in a warm area.
Allow dough to rise for 30 minutes.
Preheat the oven to 425 degrees.
Bring water to boil in a large pot over medium high heat and add in baking soda.
Cut dough into 14 pieces.
Roll each section into long ropes about 18-20inches long.
Wrap each hotdog starting at one end working to the other. Pinch the dough onto itself at the ends to hold it in place.
Place 2 to 3 wrapped hot dogs at a time into the boiling water. Boil for 20-30 seconds each.
Remove pretzel dogs with a slotted spoon or spatula to let the water drip off.
Place on to a baking sheet lined with parchment paper.
Whisk together the egg and water.
Brush the tops of the pretzels with the egg wash.
Sprinkle the tops with coarse salt.
Bake in preheated oven for 12-18 minutes, until the pretzel dough is a dark golden brown color.
Allow to cool for about 5 minutes.
Enjoy warm served with ketchup and mustard.