In the bowl of a stand mixer, combine the warm water, yeast, and brown sugar.
Let it sit for 5-10 minutes until the mixture is foamy.
Attach the dough hook and add the salt, bread flour, and 3 cups (720 ml) of the all-purpose flour.
Mix on low speed until a shaggy dough forms.
Gradually add more all-purpose flour, about ¼ cup at a time, until the dough pulls away from the sides of the bowl and is no longer sticky.
Knead on medium-low speed for 5-7 minutes, until smooth and elastic.
Transfer the dough to a lightly oiled bowl, cover, and let it rise in a warm place for 1 hour, or until doubled in size.
Preheat your oven to 425°F (220°C).
Line two baking sheets with parchment paper.
Punch down the risen dough and divide it into 8 equal pieces.
Roll each piece into a long rope, about 20-24 inches long.
To shape, form the rope into a 'U' shape, cross the ends over each other twice, then bring the ends down to the bottom of the 'U' to create the classic pretzel knot.
In a shallow dish, whisk together the 2 cups (480 ml) of warm water and the baking soda until it's dissolved.
Gently dip each shaped pretzel into the baking soda bath, ensuring it's fully submerged for about 20-30 seconds.
Place the dipped pretzels onto the prepared baking sheets.
Sprinkle generously with coarse sea salt.
Bake for 12-15 minutes, or until they are a deep golden brown.
Once out of the oven, immediately brush the warm pretzels with the melted vegan butter.
Serve warm!
Using part bread flour gives the pretzels an extra-chewy, bakery-quality texture that all-purpose flour alone can't replicate.
