In the bowl of an electric mixer, add the warm water, sugar, salt & dry east. let stand until foamy, about 5 minutes.
Add the flour and melted butter. Using the dough hook attachment, knead 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 for approximately 50 to 55 minutes or until the dough has doubled in size.
Preheat the oven to 450 degrees F. Line 2 half-sheet pans with parchment paper and lightly brush with the vegetable oil. Set aside.
Just before the dough is finished rising, fill a large, deep pan with 10 cups of water (a large Dutch oven or deep 4- to 6-quart saute pan work well). Stir in the baking soda. Bring to a boil.
Turn the dough out onto a slightly oiled work surface and divide into 8 equal pieces. About 4.5 ounces each. Optional: Use a kitchen scale to be more accurate.
Roll each piece into a long rope about 25-inches in length. Grasping both ends, bring them up slightly and towards each other, forming an oval, then cross one end over the other. Press the ends together at the bottom of the oval shape, forming a pretzel. Repeat with the remaining pieces of dough.
Place onto the parchment-lined half sheet pan.
Carefully drop three pretzels into the boiling water; 1 by 1, for 30 seconds.
Using a large spatula, carefully remove them from the water and place them back on the parchment paper-lined baking sheets. Brush the top of each pretzel with the beaten egg yolk and water mixture and sprinkle with the pretzel salt.
Bake the pretzels for about 12 to 14 minutes, or until the are a rich golden brown, rotating the pan about halfway through the baking time.
Transfer to a cooling rack for at least 5 minutes before serving.