In a small bowl, combine 1/4 cup warm water and 1/2 teaspoon brown sugar. Add yeast and stir to dissolve. Let sit 5 to 10 minutes until slightly foamy.
In a large bowl or bowl of a stand mixer, stir remaining 1 1/2 teaspoons brown sugar, both flours and salt until combined. Add yeast mixture and remaining 3/4 cup warm water; stir until a dough forms.
Knead dough by hand on a lightly floured surface 5 to 10 minutes until smooth, satiny and elastic; OR, knead dough with dough hook attachment in stand mixer on medium speed 5 minutes until smooth, satiny and elastic. Shape dough into a ball and place in a large bowl lightly greased with oil or cooking spray. Cover bowl with lightly greased plastic wrap and let dough rise in a warm place 1 hour until doubled.
Line 2 baking sheets with parchment paper. Punch down risen dough and divide into 24 equal pieces. Roll each piece into a roughly 9-inch-long rod (about 1/4-inch wide) and place 1 inch apart on prepared baking sheets. Cover loosely with lightly greased plastic wrap or a lightweight kitchen towel and let rise 30 minutes.
Meanwhile, heat oven to 350°F. Prepare the baking soda bath: In a large saucepan, bring water to a simmer over medium-high heat. Add baked soda* and 1/4 cup brown sugar; stir to dissolve.
Carefully drop a few dough rods into simmering bath. Poach 15 seconds, then remove with a slotted spoon or tongs and return to lined baking sheet. Repeat with remaining dough rods.
Brush tops of rods with egg wash, then sprinkle with salt. Bake 33 to 38 minutes, rotating pans halfway through baking, until rods are a deep golden brown and hardened. Cool pretzels completely on pans.
Fully cooled pretzel rods can be stored in an airtight container at room temperature for up to 1 week.