In a large bowl, combine warm water and yeast. Stir gently and let sit for about 5 minutes until foamy.
Stir in salt and sugar. Gradually add all-purpose flour, mixing until a shaggy dough forms.
Turn dough onto a lightly floured surface and knead for 5-7 minutes until smooth and elastic.
Lightly grease the mixing bowl, add the dough, turn to coat, cover, and let rise in a warm spot for about 1 hour, or until doubled in size.
While the dough rises, preheat oven to 450°F (230°C). Line a baking sheet with parchment paper. Bring 6 cups of water to a rolling boil in a large pot.
Carefully stir the baking soda into the boiling water. Keep at a gentle boil.
Once dough has risen, punch it down and divide into 8 equal pieces.
Roll each piece of dough into a rope about 20-24 inches long. Form a U-shape, cross the ends twice, and press onto the bottom curve to seal. Repeat for all pieces.
Gently lower one pretzel at a time into the boiling baking soda water. Boil for 30 seconds per side (1 minute total). Use a slotted spoon to transfer to the prepared baking sheet.
Brush the tops of each boiled pretzel generously with the beaten egg wash. Immediately sprinkle generously with coarse salt.
Bake in the preheated oven for 12-15 minutes, or until golden brown.
Immediately after baking, brush with melted butter (optional). Let cool on the baking sheet for a few minutes before serving warm.