In a large mixing bowl, stir together first 8 ingredients.
Mix by hand or with a stand mixer fitted with a dough hook until it forms a dough.
Knead until smooth and elastic, about 5 minutes with a stand mixer (dough will be slightly sticky, if dry, knead in additional water 1 tablespoon at a time until desired consistency).
Remove dough from bowl and shape into a ball. Clean and dry bowl and lightly grease. Place dough ball back inside clean bowl; cover the bowl and let dough rest for about 1 hour at room temperature.
Turn dough out onto a lightly greased surface and fold and shape into a rectangle. Divide equally into 12 pieces.
Cover pieces with plastic wrap while working. Roll out one piece at a time into a rope about 18 inches long.
Loop and twist each rope into a pretzel shape. Place on baking sheet while you finish rolling out and shaping the remaining pretzels.
Preheat oven to 450 degrees.
Bring 3 cups water to a boil, reduce to a medium-low boil and stir in baking soda until dissolved.
Lower one pretzel at a time into the boiling water bath for 30 seconds, flipping halfway through.
Remove using a large flat spatula and place on half sheet pans.
In a small bowl, beat together 1 egg and 1 tablespoon water. Brush each pretzel with egg wash mixture and sprinkle with coarse salt.
Bake for 12 to 15 minutes or until dark golden brown.
Remove from oven and brush each pretzel with melted butter.
Cool for 5 minutes before serving.