In the bowl of a stand mixer fitted with the dough hook, combine the water, sugar and salt. Sprinkle the yeast on top and let it sit for 5 minutes, or until it begins to foam.
Add the flour and melted butter to the bowl and mix on low speed until a dough ball begins to form, then increase the speed to medium and knead the dough until it pulls away from the sides of the bowl, 2 to 3 minutes. Remove the dough from the bowl then grease the bowl with vegetable oil and return the dough to it. Cover it with plastic wrap and set it in a dark, warm place to proof until it doubles in size, about 1 hour.
Preheat the oven to 450ºF. Grease a 10-inch cast-iron skillet or 13x9-inch baking pan with butter. Line a baking sheet with parchment paper then grease the parchment paper with butter.
In a large stockpot, whisk together the water and baking soda. Bring the mixture to a rolling boil. While the mixture is coming to a boil, uncover the dough, transfer it to your work surface and divide it into 16 equal portions. Cupping your hand over each piece of dough, roll it into a ball then set it on the greased baking sheet.
Working in batches, boil the rolls in the baking soda mixture for 30 seconds, flipping them once. Using a slotted spoon or spider, transfer the rolls back onto the baking sheet.
Arrange the rolls in a single layer in the cast-iron skillet or baking dish. Brush the tops of the rolls with the egg wash, then sprinkle them with salt.
Bake the rolls until they are dark golden brown on top and cooked through, 15 to 18 minutes. Remove them from the oven and serve.