1. Activate the Yeast: In a large bowl, combine the warm water, granulated sugar, and active dry yeast. Stir gently and let it sit for about 5-10 minutes, until the mixture becomes foamy. This indicates your yeast is active and ready to work.

2. Combine Wet Ingredients: To the foamy yeast mixture, add your sourdough discard and melted butter. Stir well until everything is thoroughly combined and the discard is mostly incorporated into the liquid.

3. Form the Dough: Gradually add the all-purpose flour and salt to the wet ingredients, mixing with a wooden spoon or your hands until a shaggy dough forms. Turn the dough out onto a lightly floured surface and knead for about 5-7 minutes until it’s smooth and elastic. It should spring back slightly when poked.

4. Shape the Bats: Divide the dough into 12-16 equal pieces. Roll each piece into a thin rope, about 10-12 inches long. To form a bat, create a loop at one end, then bring the other end over and through the loop, twisting it to form the “wings.” Pinch the ends to secure them and shape them to resemble bat wings. Alternatively, you can simply make traditional pretzel shapes if you prefer.

5. Prepare the Water Bath: Preheat your oven to 425 F (220 C). In a large pot, bring the 4 cups of water to a rolling boil. Carefully add the baking soda to the boiling water (it will foam up significantly, so use a large pot).

6. Boil and Bake: Gently drop 2-3 pretzel bats into the boiling baking soda solution for about 30 seconds per side. Using a slotted spoon, remove them and place them on a baking sheet lined with parchment paper. Brush the tops of the boiled pretzels with the beaten egg wash and sprinkle generously with coarse sea salt.

7. Bake to Golden Perfection: Bake for 12-15 minutes, or until the pretzel bats are beautifully golden brown and puffed up. Remove from the oven and transfer to a wire rack to cool slightly before serving.