Add the yeast and 1 1/2 cups of warm water to a bowl, whisk and set aside for 5 minutes. Stir in the sea salt, brown sugar, and melted brown butter, whisk gently until combined.
Begin adding the flour a scoop at a time, mixing with a wooden spoon after each addition. The dough will be very sticky at first, keep adding the flour a cup at a time until it is no longer sticky. Touch the dough with your finger and once it bounces back it's ready to knead.
Turn out onto a lightly floured counter top or cutting board and knead for 3 minutes. Shape into a ball and place in a lightly oiled (olive oil) mixing bowl. Cover with a kitchen towel and allow to rest for 10 minutes.
Preheat oven to 425°F /218°C) line 2 baking sheets with parchment paper and set aside. Add the reserved 9 cups of water and 1/2 cup of baking soda to a heavy-bottomed pot, turn on the heat and begin to bring to a boil.
Meanwhile, turn the dough out of the bowl back onto your work surface, and cut into 6 portions.
Roll each of the dough balls into approximately 20-inch ropes.
Cut the ropes into 1.5-inch pieces to make your pretzel bites.
Now that your water has come to a boil, begin dropping in pretzel bites 10-15 at a time and boil for 20-30 seconds. No longer as a metal taste can develop.
Lift the bites out of the boiling water and place onto the prepared baking sheet, making sure they all have a little elbow room.
Now beat the egg and brush over the tops of the pretzel bites, sprinkle with coarse ground Kosher sea salt. Bake in the oven for 20 minutes or until golden brown.