Place the brown sugar and warm water into a large bowl and mix until the sugar dissolves. Sprinkle the yeast over the water and let stand until foamy, about 5 mins.
Using a fork, stir in the oil, one tbsp of salt, and 1 ½ cups of flour.
Mix in the remaining flour, transfer to a floured surface and knead until smooth. If the dough is too sticky, gradually add more flour until silky smooth.
Place the dough into a large, greased bowl and cover with plastic wrap. Let rise in a draft-free place and at room temperature until doubled in size, about 45 mins to 1 hour.
Cover two baking sheets with parchment paper and grease the parchment paper. You can also use silpat mats.
Punch the dough down, turn it onto a floured surface, cut it into 12 pieces and roll each piece into 9-inch sticks about ½-inch thick. Place the sticks on the baking sheets and let rise, uncovered, for 25 mins.
Preheat the oven to 450 F and place the oven rack in the center of the oven.
Place a cooling rack on a third baking sheet.
Pour two quarts of water into a large, high-sided skillet and stir in the baking soda. Bring to a simmer and place 6 sticks into the water for 30 seconds. Transfer them to the rack to drain them. Repeat with the remaining 6 sticks.
Place the dry sticks on the baking sheets with the greased parchment paper ( 6 on each sheet), brush them with egg wash, and sprinkle flaky salt over them. Bake them for 8 to 10 minutes or until brown. Serve with yellow mustard.