1. Prepare the Dough: In a large mixing bowl, combine the sourdough discard, granulated sugar, salt, warm water, and olive oil. Mix until well combined. Gradually add the all-purpose flour, one cup at a time, mixing until a shaggy dough forms. Turn the dough out onto a lightly floured surface and knead for 5-7 minutes until it’s smooth and elastic. It should spring back slightly when poked. Lightly grease the bowl with a little olive oil, place the dough back in, cover with a clean kitchen towel or plastic wrap, and let it rest in a warm place for 30 minutes. This short rest helps the gluten relax, making the dough easier to work with.

2. Shape the Pretzels: After the rest, divide the dough into 10-12 equal pieces. Roll each piece into a long rope, about 18-20 inches long and ½ inch thick. To form the pretzel shape, make a U-shape with the rope, then cross the ends over each other twice. Bring the ends down and press them firmly onto the bottom curve of the U to secure the shape. Place the shaped pretzels on a parchment-lined baking sheet.

3. Prepare the Water Bath and Oven: Preheat your oven to 425 F (220 C). In a large pot, bring 8 cups of water to a rolling boil. Carefully stir in the baking soda until it dissolves. This baking soda bath is crucial for giving pretzels their characteristic chewy crust and golden-brown color.

4. The Baking Soda Dip: Using a slotted spoon or spatula, carefully lower one pretzel at a time into the boiling baking soda solution. Let it cook for 20-30 seconds per side. Do not overcrowd the pot; work in batches. Remove the pretzel from the water bath, letting excess water drip off, and return it to the parchment-lined baking sheet.

5. Egg Wash and Bake: Once all pretzels have been through the baking soda bath and are on the baking sheet, brush the tops with the beaten egg and generously sprinkle with coarse sea salt. Bake for 12-15 minutes, or until the pretzels are deeply golden brown and puffed. The color is your best indicator of doneness.

6. Make the Cheese Dip: While the pretzels are baking, prepare the cheese dip. In a medium saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1 minute, stirring constantly, to create a roux. Gradually whisk in the milk, ensuring no lumps form. Bring the mixture to a simmer, stirring, until it thickens slightly. Remove from heat and stir in the Dijon mustard, garlic powder, black pepper, and cayenne pepper (if using). Add the shredded cheddar cheese and stir until it’s completely melted and smooth. Keep warm until ready to serve.

7. Serve Warm: Once the pretzels are out of the oven, let them cool for a few minutes on the baking sheet before transferring them to a wire rack. Serve immediately with the warm, creamy cheese dip.