Combine the warm water (1 cup + 2 Tbsp) and brown sugar in the bowl of a stand mixer fitted with a 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, salt, and butter, and mix on low speed until well-combined. Increase to medium speed and continue to knead until a smooth dough forms, about 4-5 minutes (you can also knead by hand).
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.
Oil a large bowl and transfer the dough in a ball to the bowl. Cover with plastic wrap and let sit for 60-90 minutes, or until doubled in size.
Turn the dough out onto a smooth, dry work surface (no need to flour or oil, you'll want some traction). Divide into 8 equal pieces. Roll each piece into a 24-inch rope**. 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. Place on the parchment-lined baking pan and cover with plastic wrap or a clean kitchen towel while you prepare the next step.
Preheat the oven to 450°F. Line 2 half-sheet baking trays with parchment paper and set aside. Bring 10 cups of water and ⅔ cup baking soda to a boil in a large pot.
Place the pretzels in the boiling water, one by one, for 20-30 seconds on each side. The pretzels should float (called "passing the float test"); if not, see notes section below. Remove the pretzels from the water using a slotted spatula, shake off excess water, and return to the baking sheet.
Bake until golden brown, approximately 13-15 minutes. Transfer to a cooling rack to cool.
While the pretzels cool, melt the 4 Tablespoons butter for the topping and mix together the granulated sugar and cinnamon in a small bowl. Brush the cooled pretzels with melted butter, then sprinkle with the cinnamon sugar mixture. Serve immediately.
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Notes
*You can make this recipe without a stand mixer. To do so, mix the dough in a large bowl with a wooden spoon and knead by hand. **If you'd rather make a different shape or pretzel bites, you can! To make pretzel bites, roll the dough into a rope, then cut into bite-sized pieces. 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 or a clean kitchen towel 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 are sinking). To make this recipe with active sourdough starter, omit the yeast and replace the sourdough discard with active starter (200g). You will also need to increase the rise times.