In a small bowl, combine warm water, sugar, and yeast. Let it sit for about 5 minutes until frothy.
In a large mixing bowl, combine flour and salt.
Pour the yeast mixture into the flour mixture and stir until a dough forms.
Knead the dough on a floured surface for about 5-7 minutes until smooth.
Place the dough in a greased bowl, cover with a towel, and let it rise in a warm place for about 1 hour or until doubled in size.
Preheat the oven to 425°F. Line a baking sheet with parchment paper.
In a large pot, bring 10 cups of water and baking soda to a boil.
Punch down the risen dough and divide it into 8 equal pieces.
Roll each piece into a long rope (about 24 inches) and shape into a pretzel.
Carefully place each pretzel into the boiling water for about 30 seconds, then remove with a slotted spoon and place on the prepared baking sheet.
Brush each pretzel with the beaten egg and sprinkle with coarse sea salt.
Bake in the preheated oven for 12-15 minutes or until golden brown.
Remove from the oven and brush with melted butter while still warm.