In the KitchenAid bowl mix the water, salt, and sugar until combined. Add yeast, and let rest 5 minutes until yeast starts to foam.
Add flour and melted butter to the bowl. Then mix in the KitchenAid using the dough hook on speed 2 until a dough ball forms and then an additional 5 minutes on speed 4 - 6 after the dough ball forms.
Remove the dough ball from the bowl, clean the bowl, and lightly coat the interior of the bowl with oil.
Place the dough ball back into the bowl, cover, and leave in a warm place for 1 hour.
Preheat oven to 450°F.
Put water and baking soda in a large pot of water and bring to a rolling boil.
Cut dough into 8 equal pieces and roll them out into thin ropes, twisting the two ends to form a pretzel shape.
Boil each pretzel for 30 seconds per side.
Transfer pretzels to a baking sheet lined with parchment paper, brush with egg wash, and then sprinkle with coarse salt. Bake for 15 minutes, spinning the pan halfway through, until golden brown.