Combine the water and sugar in the bowl of a stand mixer. Sprinkle the yeast on top and let it sit for 10 minutes or until foamy.
Once foamy, mix in the salt, flour, and melted butter and use the dough hook to mix on low until combined. Mix for 4-5 minutes or until dough begins to pull away from the bowl. You may need to use a spatula to coax the flour on the sides of the bowl into the mixture.
Lift the dough up from the side of the bowl and spray oil onto the side, repeat for the other side. Cover with a dish towel or plastic wrap and let sit for an hour to rise so it is doubled in size.
Preheat the oven to 450 degrees F. Line a baking sheet with a silpat or parchment paper.
Bring the water and baking soda together to a rolling boil in a large stockpot.
Flour your work surface. Divide the dough into 4 pieces and roll each one into a rope. Use a bench cutter or knife to cut at 1" intervals. Drop the dough pieces into the now boiling water, making sure not to crowd the pot. Plan on at least 2 separate batches, depending on the width of your pot.
Use a spider or slotted spoon to remove boiled dough once they float, or after 30 seconds. Place the boiled dough pieces, spaced out, on the baking sheet.
Beat the egg and 1 tablespoon of water together and brush over the top of each piece. Sprinkle with a little sea salt.
Bake in preheated oven for 12-14 minutes or until your desired level of golden brown.
Let cool on a wire rack for 5 minutes, then serve with dipping sauce.
Keep any leftovers sealed in a container in the fridge (after cooling) for up to 3 days.