Stir the sugar and yeast into the warm water and let sit for 5 minutes, until foamy on top.

In a large bowl, combine the flour and salt, pour in the yeast mixture and melted butter, then stir and knead on a floured surface for about 5 minutes, until the dough is smooth and springs back when poked.

Place the dough in a greased bowl, cover and let rise in a warm spot for 15 minutes, until slightly puffed (it will not double in this short rise, and that's fine).

Preheat the oven to 450°F and line 2 baking sheets with parchment.

Bring 8 cups water and the baking soda to a boil in a wide pot.

Divide the dough into 10 pieces and roll each into a 14-inch rope.

Shape each rope into a heart by curling both ends into loops at the top and pinching the tails together at the bottom point.

Drop each pretzel heart into the boiling water bath for 20 seconds, then lift out with a slotted spoon and set on a baking sheet.

Brush each with the egg wash and sprinkle with coarse salt.

Bake for 10 to 12 minutes, until deep mahogany brown, the same color as a classic soft pretzel.

Cool for 5 minutes on the pan before moving; the crust firms as it cools.

Serve warm with mustard or cheese dip on the side.