Activate yeast: Stir warm water with sugar and yeast. Let foam for 5–10 minutes.
Mix dough: Add melted butter and salt. Gradually add flour until a soft dough forms.
Knead on a lightly floured surface until smooth and elastic, 5–7 minutes.
Let rise in a greased bowl, covered, until doubled, about 45 minutes.
Preheat oven to 450°F. Line two baking sheets with parchment and lightly grease.
Make bath: Bring water to a gentle simmer. Slowly stir in baking soda.
Shape: Punch down dough. Divide into 8 pieces. Roll each to a 20–24 inch rope and twist into pretzels.
Dip each pretzel in the soda bath for 20–30 seconds. Drain well and set on sheets.
Top with coarse salt. Bake until deeply golden, 12–14 minutes.
Brush hot pretzels with melted butter. Cool a few minutes and serve warm.