In a large bowl, combine warm water, brown sugar, and yeast. Let sit for 5 minutes until foamy.
Stir in the sourdough discard until fully mixed.
Add flour and salt. Mix until a dough forms, then knead for 6-8 minutes until smooth and elastic.
Cover the dough and let rise in a warm spot for 45 minutes, or until puffy.
Preheat oven to 425°F (220°C). Line a baking sheet with parchment paper.
Bring a large pot of water to a boil and add baking soda carefully.
Divide the dough into 6 sections. Roll each into a rope and cut into 1-inch pieces.
Working in batches, drop the bites into boiling water for 30 seconds. Remove with a slotted spoon and place on the baking sheet.
Brush the pretzel bites with beaten egg and sprinkle with coarse salt.
Bake for 12-15 minutes, or until golden brown.
