Combine the warm water (1 cup + 2 Tbsp) and brown sugar in the bowl of a stand mixer fitted with the dough hook attachment. Sprinkle the yeast on top and let sit for 5 minutes or until the yeast begins to foam.

Add the sourdough discard, flour, and salt and mix on low speed. While the mixer is running, pour in the melted butter and mix until combined. Change to medium speed and continue to knead until a smooth dough forms, about 4-5 minutes.

Transfer the dough in a ball to a large, oiled bowl. Cover with plastic wrap and let sit for 60-90 minutes, or until doubled in size.

Line a half-sheet baking pan with parchment paper or a Silicone baking mat and set aside.

Turn the dough out onto a smooth, dry work surface. Roll the dough into a long rope, at least 48 inches long. Make a U-shape with the rope, then cross the ends of the rope over each other like a heart. Twist the ends together and push down at the bottom of the U. Transfer to the prepared baking sheet. Cover with plastic wrap or a clean kitchen towel and let rise for 30 minutes.

Preheat the oven to 450°F. Combine 8 cups of water and ½ cup baking soda in a large sautée pan. Stir until dissolved and bring to a boil. Remove from heat and set aside to cool until it's a temperature you can comfortably put your hands into.

Carefully place the pretzel in the cooled baking soda water bath. Using your hands or a large spoon, gently 'dunk' the pretzel continuously so it's coated on all sides by the baking soda water for 30-60 seconds.

Carefully remove the pretzel from the water bath and transfer to a cooling rack to drain off any excess water. Then, transfer the pretzel back to your parchment paper-lined baking sheet. While wet, reshape the pretzel as needed. Brush the pretzel with the egg wash and sprinkle with flaky sea salt.

Bake until golden brown, approximately 15-17 minutes. Transfer to a cooling rack to cool fully. Serve with your favorite dipping sauces.