In a large bowl or the bowl of a stand mixer, combine the sourdough starter, water, all-purpose flour, melted butter, sugar, and salt. Mix until a shaggy dough forms. Knead the dough ingredients by hand or using a stand mixer with a dough hook attachment until it's smooth and elastic, about 8-10 minutes.
Place the dough in a lightly greased bowl, cover it with plastic wrap or a damp cloth, and let it rise in a warm place for about 4-8 hours, or until it has doubled in size. (This will vary depending on strength of starter, room temperature, etc.)
Preheat your oven to 450°F. Line two baking sheets with parchment paper. Punch down the risen dough, dump it on a greased or floured surface and cut it into 8-10 equal pieces.
Roll each piece into a long rope, about 18-20 inches long. Shape each rope into a pretzel shape by forming a U-shape, crossing the ends over each other, and pressing them onto the bottom of the U.
Let them sit and rest for 15-20 minutes while you prepare the water bath.
In a wide pot or skillet, bring 6-8 cups of water to a boil. Carefully add the baking soda (it will fizz up).
Gently drop the shaped pretzels 2 or 3 at a time into the baking soda bath for about 30 seconds, flipping them halfway through. Using a slotted spatula, transfer the pretzels to the prepared baking sheet.
Whisk the egg and brush the pretzel with it using a pastry brush, then sprinkle pretzel salt over them.
Bake the pretzels in the preheated oven for 12-15 minutes, or until they are golden brown.
Brush the final product with melted butter if you wish.