Combine the water, sugar, salt, and yeast in the bowl of a stand mixer fitted with the paddle attachment. Mix on low speed to dissolve the yeast.
Add in the flour and melted butter and mix just until the dough comes together.
Switch to the dough hook and knead on medium speed until the dough is smooth and clears the sides of the bowl, about 5 minutes.
Transfer the dough to a bowl lightly greased with vegetable oil, turning once to coat. Cover with plastic wrap and let rise in a warm place, about 50-55 minutes or until doubled in bulk.
Preheat the oven to 450 degrees F. Line two baking sheets with parchment paper and spray lightly with cooking spray.
Bring the water and baking soda to a boil in a large saucepan or stockpot.
Turn the dough out onto a lightly floured work surface and gently deflate it. Divide it up into approximately 6 equal portions.
Working with one piece at a time, roll the dough out into a long rope about 1-inch in diameter. Use a pizza cutter to cut the rope into small segments, no longer than 1-inch each.
Place the pretzel bites into the boiling water in batches so that they aren’t overcrowded. Boil each batch for about 30 seconds, stirring once or twice to submerge all surfaces in the water.
Remove from the water with a slotted skimmer and spread out on the prepared baking sheets.
Once all the pretzels have been boiled, brush the tops with the egg wash and sprinkle lightly with salt.
Bake in a preheated oven until dark golden brown, about 9-11 minutes.
Transfer to a cooling rack for at least 5 minutes before serving. Serve with mustard.