In the bowl of a stand mixer fitted with a dough hook, whisk together the warm water and brown sugar. Sprinkle the yeast over top and let sit for 5 to 7 minutes until frothy.

Add the flour, fine salt, and 2 tablespoons of melted butter. Mix on low speed until a shaggy dough forms, then increase to medium-low and knead for 5 minutes until smooth and elastic.

Form the dough into a ball, place in an oiled bowl, cover with a clean kitchen towel, and let rise in a warm spot for 50 to 60 minutes until doubled in size.

Preheat your oven to 450°F (230°C). Line two large baking sheets with parchment paper and grease the paper lightly with oil.

Bring 9 cups of water and 1/2 cup of baking soda to a rolling boil in a wide pot.

Turn the dough onto a lightly oiled work surface. Divide into 8 equal portions. Roll each piece into a 22-inch long rope. Shape into a pretzel by creating a U-shape, crossing the ends over each other twice, and folding the ends down onto the bottom curve.

Drop 1 to 2 pretzels at a time into the boiling baking soda bath for 30 seconds. Remove with a slotted spatula, drain excess water, and place on the prepared baking sheets.

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

Bake at 450°F for 12 to 15 minutes until deeply golden brown. Brush immediately with melted butter and serve warm.