1. Activate the Yeast and Sourdough: In a large mixing bowl, combine the warm water, granulated sugar, and active dry yeast. Stir gently and let it sit for 5-10 minutes until the yeast is foamy on top. This foam indicates the yeast is alive and active. Then, stir in the sourdough discard until well combined.

2. Form the Dough: Add the all-purpose flour and fine sea salt to the wet ingredients. Mix with a wooden spoon or your hands until a shaggy dough forms. Turn the dough out onto a lightly floured surface and knead for 5-7 minutes until it becomes smooth and elastic. It should spring back slightly when poked.

3. First Rise (Bulk Fermentation): Place the kneaded dough in a lightly oiled bowl, turning it once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm spot for 60-90 minutes, or until it has nearly doubled in size. The dough should feel puffy and soft.

4. Shape the Buns: Gently punch down the risen dough to release the air. Divide the dough into 8-10 equal pieces. Roll each piece into a smooth ball, then flatten it slightly into a disc. You can leave them as round buns or gently shape them into more elongated oval shapes if you prefer. Place the shaped buns on a parchment-lined baking sheet.

5. Prepare the Baking Soda Bath: Preheat your oven to 400 F (200 C). In a large pot, bring 8 cups of water to a rolling boil. Carefully add the 1/2 cup of baking soda to the boiling water. Be cautious as it will foam up significantly.

6. The Pretzel Bath: One or two at a time, carefully drop the shaped buns into the boiling baking soda solution. Let them simmer for 30 seconds on each side. Use a slotted spoon to remove them, allowing excess water to drain, and return them to the parchment-lined baking sheet.

7. Egg Wash and Bake: Brush the tops of the boiled buns generously with the beaten egg wash. Immediately sprinkle with coarse sea salt. Using a sharp knife or razor blade, make a shallow “X” cut on the top of each bun. Bake for 15-20 minutes, or until the buns are deep golden brown and sound hollow when tapped on the bottom.

8. Cooling: Transfer the baked pretzel buns to a wire rack to cool slightly before serving. They are best enjoyed warm.