Combine warm water, sugar, and salt in the bowl of a stand mixer then sprinkle the yeast on top. Let sit for 5 minutes or until foaming.
Add the flour and melted butter and, using the dough hook attachment, mix on low speed until well combined. Change to medium speed and knead until the dough is smooth and pulls away from the side of the bowl, approximately 4 to 5 minutes.
Remove the dough from the bowl, clean the bowl and then oil it well with vegetable oil. Return the dough to the bowl, cover with plastic wrap and sit in a warm place until the dough has doubled in size, approximately 50 to 55 minutes.
Preheat the oven to 450 degrees F. Line 2 half-sheet pans with parchment paper, set aside.
Bring the 10 cups of water and the baking soda to a rolling boil in a large saucepan.
In the meantime, turn the dough out onto a slightly oiled work surface and divide into 8 equal pieces. Roll out each piece of dough into a 12-inch rope. Cut each rope into 5 bite-sized pieces.
Place the pretzel bites into the boiling water, for 15-20 seconds. Remove them from the water to a clean dish towel, then onto the prepared baking sheet. Brush the top of each pretzel with the beaten egg yolk mixture and sprinkle with pretzel salt. Bake until dark golden brown in color, approximately 12 to 14 minutes. Transfer to a cooling rack for at least 5 minutes before serving.
