In a large bowl or the bowl of a stand mixer, combine the remaining 1½ teaspoons brown sugar, both flours, and salt. Add the yeast mixture and the remaining ¾ cup warm water. Stir until a shaggy dough forms.

Knead by hand on a lightly floured surface for 5–10 minutes, or with a dough hook on medium speed for about 5 minutes, until the dough is smooth, satiny, and elastic.

Shape dough into a ball and place in a lightly greased bowl. Cover with lightly greased plastic wrap and let rise in a warm place for 1 hour, or until doubled in size.

Line 2 baking sheets with parchment paper. Punch down the dough and divide into 24 equal pieces. Roll each piece into a 9-inch-long rod, about ¼-inch thick, and place 1 inch apart on the prepared baking sheets.

Cover loosely with lightly greased plastic wrap or a clean kitchen towel. Let rest 30 minutes, until slightly puffed.

Preheat oven to 350°F. In a large saucepan, bring 8 cups water to a gentle simmer. Add ½ cup baked baking soda and ½ cup brown sugar, stirring until dissolved.

Working in batches, carefully lower a few dough rods into the simmering bath. Poach for 15 seconds, then remove with a slotted spoon or tongs and return to the baking sheets. Repeat with remaining rods.

Brush the tops of the poached rods with egg wash and sprinkle evenly with pretzel salt.

Bake for 33–38 minutes, rotating pans halfway through, until the pretzel sticks are deep golden brown and hardened.

Cool completely on the baking sheets. Pretzel sticks will continue to firm up as they cool.