1. Combine the Dough Ingredients: In a large mixing bowl, combine the sourdough discard, all-purpose flour, granulated sugar, salt, and melted butter. Mix with a sturdy spoon or your hands until a shaggy dough forms.

2. Knead Until Smooth: Turn the dough out onto a lightly floured surface. Knead for about 5-7 minutes until the dough is smooth, elastic, and no longer sticky. It should bounce back slightly when poked.

3. Shape the Dough: Divide the dough into 6-8 equal pieces. Roll each piece into a long rope, about 1/2 inch thick. Then, cut each rope into 1-inch pieces to form your pretzel bites.

4. Prepare the Water Bath: In a large pot, bring 4 cups of water to a rolling boil. Carefully add the baking soda to the boiling water. Be cautious as it will foam up significantly. Reduce the heat slightly to maintain a gentle boil.

5. Boil the Pretzel Bites: Working in small batches (about 10-15 pieces at a time), drop the pretzel bites into the boiling baking soda solution. Let them boil for 20-30 seconds, flipping them gently halfway through. They will puff up slightly. Using a slotted spoon, remove the bites and place them on a parchment-lined baking sheet.

6. Egg Wash and Salt: Preheat your oven to 400 F (200 C). Once all the pretzel bites are boiled and on the baking sheet, brush them generously with the beaten egg wash. Immediately sprinkle them with coarse sea salt.

7. Bake to Golden Perfection: Bake for 12-15 minutes, or until the pretzel bites are deeply golden brown and puffed. Keep an eye on them towards the end of baking to prevent over-browning.

8. Serve Warm: Remove from the oven and let cool for a few minutes on the baking sheet before transferring to a serving platter. They are best enjoyed warm!