1. 1. Prepare the Dough: In a large mixing bowl, combine the sourdough discard, melted butter, sugar, and salt. Mix well until everything is thoroughly incorporated. Gradually add the all-purpose flour, mixing first with a spoon and then with your hands, until a shaggy dough forms.

2. 2. Knead the Dough: Turn the dough out onto a lightly floured surface. Knead for about 5-7 minutes until the dough becomes smooth and elastic. It should feel less sticky and bounce back slightly when poked. Form the dough into a ball and let it rest, covered, for 10 minutes at room temperature. This brief rest helps the gluten relax, making the dough easier to work with.

3. 3. Shape the Pretzel Bites: Divide the dough into 4 equal pieces. Roll each piece into a long rope, about 1/2 inch thick. Use a sharp knife or a bench scraper to cut each rope into 1-inch pieces. You’ll have many small pretzel bites.

4. 4. Prepare the Baking Soda Bath: Preheat your oven to 400 F (200 C). Line two baking sheets with parchment paper. In a large pot, bring the 4 cups of water to a rolling boil. Carefully add the baking soda and stir until dissolved. The water will foam up, which is normal.

5. 5. Bathe and Bake: Working in small batches, drop the pretzel bites into the boiling baking soda solution for 20-30 seconds. Do not overcrowd the pot. Using a slotted spoon, carefully remove the bites, allowing excess water to drip off, and place them on the prepared baking sheets, leaving a little space between each.

6. 6. Egg Wash and Season: In a small bowl, whisk the egg to create an egg wash. Brush the tops of the pretzel bites with the egg wash. Immediately sprinkle generously with coarse sea salt.

7. 7. Bake Until Golden: Bake for 12-15 minutes, or until the pretzel bites are puffed up and deep golden brown. The color is important for that classic pretzel flavor and texture. Remove from the oven and let cool slightly on the baking sheets before serving.