In your stand mixer bowl, dissolve the kosher salt and the sugar in the warm water. Sprinkle yeast over the mixture and allow to foam for about 5 minutes.
Attach the dough hook. Add the flour and butter (butter should be warm but not hot) and mix on lowest setting until well combined.
On the second mixer setting, knead the dough about 5 minutes, until the dough forms a ball and cleans away from the sides of the bowl.
Oil a large bowl with the vegetable oil, making sure it is well coated.
Put the dough in the oiled bowl, cover with plastic wrap, and let rise in a warm place until doubled in size, about one hour.
Preheat oven to 450°f
Line 2 large baking sheets with parchment paper. Lightly oil each with the vegetable oil.
In a large saucepan or pot, bring the 10 cups of water to a boil. Add the baking soda.
On a baking mat or a lightly oiled surface, divide the dough into 8 equal pieces.
Roll each out into a 24-inch rope. As you work with each, keep the others covered to avoid drying out.
Form each into the pretzel shape. Make a U-shape, then bring the ends around to form the pretzel cross.
Place each on the parchment paper lined baking sheets.
One at a time, dip the pretzel into the boiling water for about 30 seconds each. Use a large spatula to remove each, placing them back onto the baking sheet.
Brush the top of each with the egg yolk mixture.
Sprinkle with pretzel salt.
Bake about 12-14 minutes. Pretzels are done when they are a deep golden color.
Remove to a cooling rack for several minutes before serving.