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 (you can also knead by hand if preferred).
If needed, add more flour or water (1 Tablespoon at a time) to reach your desired consistency. The dough should be fairly sturdy, smooth, and not sticky.
Shape the dough into a ball and transfer to a large, oiled bowl. Cover with plastic wrap and let sit for 60-90 minutes, or until doubled in size.
Line 2 half-sheet baking trays with parchment paper or a baking mat (such as a Silpat mat) and set aside.
Turn the dough out onto a smooth, dry work surface (no need to flour or oil, you'll want some traction). Divide into 16 equal-size pieces (this doesn't need to be exact). Roll each piece into a 14-16 inch rope.
Tie a soft knot at the end of the rope. There doesn't need to be any tension on the dough. Tie another soft knot at the other end of the rope. The two knots will be about 3-4 inches apart. Place the bones on the parchment paper-lined baking sheet. Continue with the remaining dough until all the bones have been shaped. Cover the pretzel bones with plastic wrap or a clean kitchen towel for 20 minutes while you prepare the next step.
Preheat the oven to 450°F (230℃). Bring 10 cups of water and ⅔ cup baking soda to a boil in a large pot. Make sure to add the baking soda to the water before it boils to avoid a bubbly mess!
Place the pretzel bones in the boiling water for about 45 seconds, dunking them occasionally, so they're coated on all sides. You'll likely be able to boil several pretzel bones at once, but make sure they have enough room to float freely. The pretzels should float (called "passing the float test"); if not, see notes section below. Remove the pretzel bones from the water using a slotted spoon or spatula and shake off excess water. Return the pretzel bones to the baking sheet. Lightly brush each pretzel bone with egg wash and sprinkle with flaky sea salt.
Bake until golden brown, approximately 13-15 minutes. Transfer to a cooling rack to cool fully. Serve with your favorite dipping sauce.
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Notes
1 serving = 2 bones. Nutrition information is an estimate and may not reflect the exact amount of sodium retained from the baking soda bath. Most of the bath is discarded before baking, but some sodium may remain on or in the pretzels.* You do not need to use a stand mixer to make this recipe. You can also make the dough in a large bowl with a wooden spoon, then knead by hand. This recipe can also be made with active sourdough starter instead of sourdough discard. To do so, omit the yeast and replace the sourdough discard with active starter (200g). You'll also need to increase the rise times. Passing the float test: When you boil the pretzels, they should float in the water. If your pretzels do not float, cover the unboiled pretzels with plastic wrap and let rise for another 10 minutes, then try again. If they are not floating, they have not risen long enough and will be dense (which is why they sink).