In the bowl of a stand mixer, combine the butter, sugar, salt and 1 ½ cups warm water. Sprinkle the yeast on top. Add the flour and mix with the dough hook attachment on low speed. Once the dough comes together, increase the speed to medium and mix for another 4 to 5 minutes, until the dough is smooth and pulls away from the sides of the bowl. Remove the dough from the bowl, wipe the bowl and then spray with the vegetable oil. Return the dough to the bowl, turning once to cover both sides with the oil. Cover tightly with plastic wrap and let rise in a warm place for approximately 45-50 minutes, or until doubled in size.

Preheat the oven to 450 degrees F. Line two large baking sheets with parchment paper and lightly spray with nonstick spray; set aside.

Bring the 10 cups of water to a boil in a large sauce pan or stock pot, then add the baking soda.

While waiting for the water to boil, turn the dough out onto a slightly oiled work surface or a large pastry mat. Divide the dough into 16 pieces. Roll one of the pieces of dough into a 24-inch rope, then wrap around a hot dog, leaving the ends of the hot dog slightly exposed. Pinch the rope together at each end to seal. Place on parchment lined baking sheet. Repeat with remaining dough and hot dogs.

Working with two or three pretzel dogs at a time, boil each for 30 seconds, flipping halfway. Use a large slotted spoon or spatula to remove from the water and return to the baking sheet. Brush the top of each pretzel with the egg wash then sprinkle with kosher or pretzel salt.

Bake one sheet (8 pretzel dogs) at a time on the center rack of the oven until dark golden brown, approximately 12 to 14 minutes. Allow to cool on a wire rack for 5 minutes before serving.