In the bowl of a stand mixer fitted with a dough hook, whisk together the warm water, brown sugar, and sourdough starter until the starter is mostly dissolved.
Pour in the melted butter, bread flour, and fine sea salt.
Mix on low speed until a shaggy dough forms. Increase the mixer speed to medium-low and knead for 5-7 minutes until the dough is smooth, elastic, and pulls away cleanly from the sides of the bowl.
Cover the bowl with a damp towel or plastic wrap and let it rest in a warm spot for about 2 hours, or until the dough has noticeably puffed up and roughly doubled in size. (For a deeper flavor, you can place it in the fridge overnight after this step).
Preheat your oven to 400°F (200°C) and line two large baking sheets with parchment paper. Lightly spray the parchment with non-stick spray to prevent sticking.
Turn the dough out onto a clean, un-floured work surface.
Divide the dough into 4 equal pieces. Roll each piece into a long rope, about 1-inch thick.
Use a bench scraper or sharp knife to cut the ropes into 1.5-inch bite-sized pieces.
In a large, wide pot, bring the 8 cups of water to a rolling boil. Carefully and slowly add the baking soda (it will bubble up rapidly).
Drop the dough bites into the boiling water in batches of 8-10. Boil for 30 seconds, then use a slotted spoon to remove them, letting excess water drip off.
Place the boiled bites onto the prepared baking sheets, making sure they aren't touching.
In a small bowl, whisk the egg and 1 tablespoon of water together.
Brush the top of each pretzel bite generously with the egg wash, then immediately sprinkle with coarse pretzel salt.
Bake for 12-15 minutes, or until the pretzel bites are a deep, rich mahogany brown.
Transfer to a wire rack to cool slightly before serving warm with your favorite dips!