Activate the yeast: In a large bowl, combine the warm water, brown sugar, and fast-rising yeast. Stir and let it sit for 5-10 minutes until the yeast is bubbly and foamy.
Mix the dough: In a separate bowl, combine the flour and salt. Add the yeast mixture and melted butter. Stir until the dough comes together, then knead for about 5 minutes on a floured surface until smooth and elastic.
Let the dough rise: Cover the dough and let it rise in a warm place for 1 hour or until it doubles in size.
Shape the pretzels: Preheat your oven to 450°F (232°C). Once the dough has risen, divide it into 8-12 equal pieces. Roll each piece into a long rope and shape into a classic pretzel twist.
Prepare the baking soda bath: In a large pot, bring 10 cups of water to a boil. Add the baking soda and stir until dissolved. Carefully lower each shaped pretzel into the bath, cooking for 30 seconds per pretzel. Remove with a slotted spoon and place on a parchment-lined baking sheet.
Egg wash and baking: Beat the egg and water together for the egg wash. Brush each pretzel with the egg wash, then sprinkle with coarse sea salt. Bake the pretzels in the preheated oven for 13-15 minutes, or until golden brown.
Serve: Allow the soft pretzels to cool slightly, then serve with mustard, cheese sauce, or enjoy them as is!