Combine the warm water, yeast, and sugar. If using active dry yeast, let the mixture stand for about 5 minutes until foamy. Instant yeast may be mixed directly with the flour.

Add the fine salt, melted butter, and most of the flour. Mix until a rough dough forms, then add the remaining flour gradually until the dough is soft and slightly tacky.

Knead by hand for 5–8 minutes or with a dough hook for about 4–5 minutes. The finished dough should be smooth, elastic, and pliable rather than sticky.

Place the dough in a lightly oiled bowl, cover it, and let it rise in a warm place for 45–60 minutes, or until doubled in size.

Heat the oven to 425°F (220°C) and line baking sheets with parchment paper. Divide the risen dough into 8 pieces.

Roll each piece into a rope about 20–24 inches long. Shape each rope into a pretzel and press the ends firmly into the dough so they stay attached.

Bring 10 cups of water and the baking soda to a boil. Boil each pretzel for 20–30 seconds, turning once if needed, then transfer it with a slotted spoon to the prepared baking sheet.

Brush each pretzel with the egg wash and sprinkle with coarse salt. Bake for 12–15 minutes, until deeply golden brown, then brush with melted butter while warm if desired.