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.
Add the yeast mixture and melted butter to the flour. Mix until a dough forms.
Knead the dough on a floured surface for about 5 minutes until smooth.
Place the dough in a greased bowl, cover with a towel, and let it rise in a warm place for 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 8 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 rope about 1 inch thick, then cut into 1-inch pieces.
Carefully drop the pretzel bites into the boiling water for about 30 seconds, then remove with a slotted spoon and place on the prepared baking sheet.
Brush the tops with beaten egg and sprinkle with coarse sea salt.
Bake for 12-15 minutes or until golden brown. Allow to cool slightly before serving.