Place the brown sugar in a large bowl and pour in the warm water.
Sprinkle the yeast on top and allow it to become foamy (approx. 5 to 10 minutes).
Stir in about 2 1/2 cups of flour along with the salt, beer, and melted butter.
Continue adding flour as needed, until a stiff dough forms. (The dough should gather itself into a ball and pull cleanly away from the sides of the bowl.)
Knead the dough until it passes the windowpane test (approx. 10 to 15 minutes).*
Remove the dough from the bowl, mist the bowl with non-stick spray, then return the dough to the bowl and cover it with plastic wrap.
Allow the dough to rise until doubled in volume (approx. 90 minutes).
Punch the dough down and divide it into 8 equal portions.
Roll each portion of dough into a tight ball, press it slightly flatter, and place it on a parchment-lined baking sheet. Mist a sheet of plastic wrap with non-stick spray and allow the shaped rolls to rise until doubled in volume (approx. 30 minutes).**
Preheat the oven to 425 degrees F and bring a large pot of water to a boil.
Add the baking soda to the boiling water (be careful, it will fizz up!).
Gently place the unbaked rolls in the water (taking care not to deflate them) and allow them to boil for about a minute on each side.
Drain the boiled rolls and place them on a parchment-lined baking sheet. Brush the rolls with egg wash and sprinkle with additional salt for garnish.
Score the unbaked buns with an "x" shape, using a sharp knife or baker's lame. Bake the pretzel buns until deeply browned and shiny (approx. 20 to 24 minutes).