In a large mixing bowl, whisk the active dry yeast into warm water. Allow it to sit for 5 minutes until it becomes foamy and activated.
Add the salt, packed brown sugar, and melted butter to the yeast mixture. Whisk until all the ingredients are combined.
Slowly add 3 cups of all-purpose flour to the mixture, one cup at a time, and mix until the dough becomes thick and starts to come together.
Add 1 more cup of flour to the dough, kneading it until it is no longer sticky. You may need to add more flour if the dough is still too sticky.
Turn out the dough onto a lightly floured surface and knead it for 3 minutes until it becomes smooth and elastic.
Form the dough into a ball and place it in a greased bowl. Cover the bowl and let the dough rise for 10 minutes.
Preheat your oven to 400°F (200°C). Line two large baking pans with parchment paper and set them aside.
Divide the dough into 8 equal sections. Roll each section into a long rope, about 20 inches long.
Shape each rope into a pretzel shape and place them on the prepared baking pans.
In a large pot, combine 9 cups of water with the baking soda and bring it to a boil.
Carefully place each pretzel into the boiling water for 20 seconds. This step gives the pretzels their classic chewy texture.
Remove the pretzels from the boiling water and place them back on the baking pans.
Brush the beaten egg white over each pretzel and sprinkle them with coarse salt for added flavor and texture.
Bake the pretzels in the preheated oven for 18 minutes or until they turn golden brown.