In a small bowl, combine the warm water, yeast, and sugar. Let sit for about 5 minutes until frothy.
In a large bowl, mix the flour and salt. Make a well in the center and pour in the yeast mixture and melted butter.
Stir until the dough begins to come together, then turn it out onto a lightly floured surface and knead for about 5-7 minutes until smooth and elastic.
Place the dough in a lightly oiled bowl and cover with a damp cloth or plastic wrap. Let rise in a warm place for about 1 hour, or until doubled in size.
Preheat the oven to 450째F (230째C) and line a baking sheet with parchment paper.
Punch down the risen dough and divide it into 8 equal pieces.
Roll each piece into a long rope, then shape into a pretzel by forming a U shape and crossing the ends over each other, pressing the ends into the bottom of the U.
In a large pot, bring 4 cups of water to a boil and add the baking soda.
Carefully drop each pretzel into the boiling solution for about 30 seconds, then use a slotted spoon to transfer them to the prepared baking sheet.
Brush each pretzel with the beaten egg and sprinkle with coarse sea salt.
Bake the pretzels for about 12-15 minutes, or until golden brown.
Let the pretzels cool slightly on a wire rack before serving.
Enjoy your meal!