In the bowl of a stand mixer, combine the warm water, yeast, brown sugar, and salt. Let sit for 1–2 minutes.
Add the melted butter and bread flour. Using a dough hook, mix on low speed until a dough forms. Increase the speed to medium and knead for about 5 minutes, or until the dough is smooth and elastic. If the dough feels too sticky, add 1–2 tablespoons of additional flour.
Shape the dough into a ball, cover, and let it rest for 20 minutes.
Meanwhile, preheat the oven to 450°F and line two baking sheets with parchment paper or silicone baking mats. Prepare the baking soda bath by bringing the water and baking soda to a boil.
Divide the dough into 8 equal portions. Roll each piece into a rope about 24 inches long. Shape into pretzels by forming a U-shape, twisting the ends together, and folding them back toward the bottom.
Working one at a time, place each pretzel into the baking soda bath for about 30 seconds. Remove with a slotted spoon and place on the prepared baking sheets. The baking soda bath is what gives pretzels their signature chewy crust and deep golden color.
Whisk together the egg yolk and water. Brush each pretzel with the egg wash and sprinkle with pretzel salt.
Bake for 12–14 minutes, or until deeply golden brown.