To prepare the dough:

1. In the bowl of a stand mixer, combine the warm water and yeast. Let stand for 10 minutes, then stir to dissolve the yeast. Add 2 1/2 cups of the flour, the sugar and salt.
2. Using a stiff spatula, combine until the dough is shaggy.
3. Fit the mixer with a dough hook. Knead the dough on low speed, about 5 minutes. After beginning the kneading process, add 1 tablespoon of flour if the dough is sticky. When finished, the dough should hold in a ball shape.
4. Lightly oil a medium bowl. Transfer the dough to the bowl, cover, and store in a warm place. Allow the dough to rise until doubled, about 1 hour.

To prepare the pretzels:

1. Turn the risen dough onto a lightly floured work surface. Using a bench scraper, divide the dough into 8 equal pieces.
2. Take a piece of dough and use the palms of your hands to roll it into a long, skinny rope about 18-20 inches in length.
3. To form the classic pretzel shape, cross the ends of the pretzel rope, cross a second time to twist and fold the twisted portion over the bottom loop.
4. Transfer the pretzel to a parchment paper-lined baking sheet.
5. After all pretzels have been shaped, cover them loosely and set aside. Allow the shaped pretzels to rise until they are puffy, about 30 minutes.
6. Preheat the oven with a rack in the middle position to 450 degrees F.
7. In a large, wide pot over high heat, bring 8 cups water to a rapid simmer. The water level should be at least 3 inches below the top of the pot.
8. Add the baking soda and the dark brown sugar. Stir until the baking soda and brown sugar has dissolved. Reduce heat to medium so water returns to a light simmer.
9. Working in batches, carefully lower 2-3 pretzels into the water bath. Simmer for 30 seconds or so. Use a slotted spoon to flip the pretzels. Simmer for another 30 seconds. Transfer the boiled pretzels to the prepared baking sheet.
10. Brush the boiled pretzels with the egg, and sprinkle with salt.
11. Bake the pretzels until the are browned, about 15 minutes.
12. Transfer baked pretzels to a cooling rack until cool enough to eat.