For the pretzels, combine 1 1/2 cup of water, 2 Tbsp light brown sugar, and the active dry yeast in the electric stand mixer bowl, and mix using the dough hook attachment. Let sit for 5 minutes to activate. The water temperature should be between 110°F – 115°F. If the water is too hot, it will kill the yeast.
Add the melted butter to the water, yeast, and brown sugar, and mix together. Add in the salt and the flour and mix on low speed until the dough is starting to form. Increase the speed to medium, and continue kneading the dough until it becomes smooth and starts to pull away from the edges of the bowl, about 4-5 minutes. You may want to use a rubber spatula to scrape down the edges. If dough appears wet, add flour and continue to knead in the mixer.
Flour a flat surface where you can knead the dough. Place the dough on the floured surface, and knead by hand for 3-4 minutes. Form the dough into a ball and place it into an oiled bowl. Flip the dough ball over so that all sides of the dough ball are lightly coated with oil. Place a warm damp towel over the bowl and let it rise for about an hour. The dough should double in size.
Preheat the oven to 325 °F. Place your 3 quarts of water in a pot on the stove on high heat and allow it to begin to start boiling.
Remove the dough from the bowl, and place it on a flat surface. Divide dough into 8 equal pieces. Roll each piece of dough into an even rope, approximately 18-20 inches long. Cut the dough into one-inch pieces.
Carefully and slowly add the baking soda to the boiling water so that it does not boil over. Boil the pretzel bites for 45 seconds, then remove them with a slotted spoon. Place the pretzels on a baking sheet lined with parchment paper. If you do not have parchment paper, make sure your grease your pan so that the pretzels do not stick. Brush the pretzels with the egg wash, and sprinkle them with coarse salt.
Bake the Pretzels for 16-18 minutes, or until they are golden brown.