Combine warm water, sugar, and yeast in a large bowl. Stir and leave 5–10 minutes until foamy. If no foam forms, start over with fresh yeast.
Add softened butter and salt to the yeast mixture. Add bread flour one cup at a time, stirring between additions until a rough dough forms. Turn onto a lightly floured surface and knead 8–10 minutes until smooth and elastic. Alternatively, use a stand mixer with dough hook on medium for 6 minutes.
Place dough in a lightly oiled bowl and cover with plastic wrap. Leave in a warm spot for 1 to 1.5 hours until doubled in size.
Punch dough down and divide into 10–12 equal pieces. Flatten each piece, pull edges to the center, and pinch to seal at the bottom. Place seam-side down on parchment-lined baking sheets. Cover loosely and rest 20 minutes.
Bring 8 cups of water to a boil. Add baking soda carefully — it will foam briefly. Reduce to a gentle boil. Working in batches, lower each roll in with a slotted spoon and cook 30 seconds per side. Return to the baking sheet.
Preheat oven to 425°F. Brush each roll with egg wash. Score an X or two parallel cuts across the top with a sharp knife. Sprinkle generously with coarse salt. Bake 18–22 minutes until deep mahogany brown. Brush with melted butter immediately out of the oven if desired.
