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

2. Knead the Dough Until Smooth: Turn the dough out onto a lightly floured surface. Knead for about 8-10 minutes, or until the dough is smooth, elastic, and no longer sticky. It should spring back slowly when poked.

3. Allow the Dough to Rest: Place the kneaded dough back into the lightly oiled bowl, turning it once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rest in a warm place for 1-2 hours, or until it has visibly increased in size (it doesn’t need to double, just become puffy). This is a shorter rest than a typical sourdough, designed for a quicker snack.

4. Shape the Pretzels: Gently punch down the dough and divide it into 8-10 equal pieces. On a lightly floured surface, roll each piece into a long rope, about 18-24 inches long and 1/2 inch thick. Form each rope into a U-shape, cross the ends over each other, and then twist them once more before bringing them down to attach to the bottom of the U, forming the classic pretzel shape.

5. Prepare the Baking Soda Bath: Preheat your oven to 425 F (220 C). Line a large baking sheet with parchment paper. In a wide, shallow pot, bring 8 cups of water to a rolling boil. Carefully add the 1/2 cup of baking soda. The water will foam up, so be cautious.

6. Boil and Bake the Pretzels: Using a slotted spoon, carefully drop one or two pretzels into the boiling baking soda bath for 20-30 seconds per side. Do not overcrowd the pot. Remove the pretzels, letting excess water drip off, and place them on the prepared baking sheet. Repeat with the remaining pretzels.

7. Egg Wash and Salt: In a small bowl, whisk the large egg to create an egg wash. Brush the top of each boiled pretzel generously with the egg wash, then immediately sprinkle with coarse sea salt.

8. Bake Until Golden Brown: Bake for 12-15 minutes, or until the pretzels are puffed up and a deep golden brown. Transfer to a wire rack to cool slightly before serving.