In the bowl of a stand mixer fitted with the dough hook, combine the hot water, sugar and salt. Sprinkle the yeast on top of the mixture and allow it to sit undisturbed until it begins to form and puff up, 7 to 10 minutes.
Add the flour and melted butter to the bowl and mix on low speed just until combined.
Increase the speed to medium and continue mixing until the dough is smooth and pulls away from the side of the bowl, 4 to 5 minutes.
Grease a large bowl with vegetable oil. Transfer the dough from the stand mixer bowl into the greased bowl then cover it with plastic wrap. Place the bowl in a warm, dark place to allow the dough to rise and double in size, about 1 hour. (See Kelly's Note.)
Preheat the oven to 450ºF.
Line two sheet trays with parchment paper and then grease them lightly with vegetable oil.
In a large, heavy-bottom stock pot or Dutch oven set over medium-high heat, whisk together 10 cups of water with the baking soda. Bring the mixture to a rolling boil.
While the water comes to a boil, transfer the dough onto your work surface and divide it into 10 equal pieces.
Roll out each piece of dough into a 24-inch rope. Shape the ropes into pretzels then return them to the cookie sheets.
Plunge the pretzels, one by one, into the boiling water for 30 seconds. Remove each of them from the water using a large slotted spoon and return them to the cookie sheet.
Brush the pretzels with the egg wash then sprinkle them with salt (optional).
Bake the pretzels until they are dark-golden brown in color, 12 to 14 minutes. Remove them from the oven and let cool slightly before serving.