Activate the yeast: In a small bowl, combine the warm water, sugar, and yeast. Stir to dissolve and let sit for 5 minutes until frothy.

Make the dough: In a large bowl, mix the flour and salt. Add the yeast mixture and melted butter. Stir until a dough forms, then knead on a floured surface for about 5 minutes until smooth and elastic.

Let it rise: Place the dough in a greased bowl, cover with a clean towel, and let it rise for 1 hour, or until it doubles in size.

Preheat the oven: Preheat your oven to 450°F (232°C). Line two baking sheets with parchment paper.

Shape the pretzels: Punch the dough down and divide it into 8 equal pieces. Roll each piece into a long rope (about 18 inches long). Form each rope into a U shape, then twist the ends and fold them over to form a pretzel shape.

Boil the pretzels: In a large pot, bring 10 cups of water and the baking soda to a boil. Carefully drop each pretzel into the boiling water, one at a time, for about 30 seconds. Use a slotted spoon to remove the pretzels and place them on the prepared baking sheets.

Add the egg wash: Brush each pretzel with the beaten egg, then sprinkle with coarse salt.

Bake the pretzels: Bake for 12-15 minutes, or until golden brown.

Serve: Let the pretzels cool slightly before serving. Enjoy with mustard, cheese, or your favorite dipping sauce!